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## Trenkler, Götz

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 Author ID: trenkler.gotz Published as: Trenkler, G.; Trenkler, Götz Homepage: https://www.statistik.tu-dortmund.de/trenkler.html External Links: MGP · Wikidata · ResearchGate · dblp · GND
 Documents Indexed: 155 Publications since 1976, including 9 Books Biographic References: 1 Publication
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#### Co-Authors

 21 single-authored 31 Baksalary, Oskar Maria 16 Trenkler, Dietrich 15 Gross, Jürgen 11 Stahlecker, Peter 9 Knautz, Henning 7 Gnot, Stanisław 7 Liski, Erkki P. 6 Baksalary, Jerzy K. 6 Schmidt, Karsten 5 Stemann, Dietmar 5 Toutenburg, Helge 5 Troschke, Sven-Oliver 4 Ihorst, Gabriele 4 Neudecker, Heinz 4 Schipp, Bernhard 4 Wei, Laisheng 3 Styan, George P. H. 2 Büning, Herbert 2 Liu, Shuangzhe 2 Pordzik, Paweł R. 2 Urbańska-Motyka, Agnieszka 2 Wijekoon, Pushba 2 Zmyślony, Roman 1 Ahmed, Syed Ejaz 1 Bernstein, Dennis S. 1 Diersen, J. 1 Farebrother, Richard William 1 Frauendorf, Eckehard 1 Freund, Eckhard 1 Hering, Franz 1 Hessenius, Helga 1 Heun Song, Seuck 1 Hunter, Jeffrey J. 1 Liu, Xiaoji 1 Markiewicz, Augustyn 1 Michels, Paul 1 Puntanen, Simo 1 Ruiz Espejo, Mariano 1 Saxena, Sharad 1 Schach, Siegfried 1 Singh, Housila Prasad 1 Tamaschke, Sabine 1 Toutenberg, H. 1 Werner, Hans-Joachim 1 Yang, Zhongpeng
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#### Serials

 23 Linear Algebra and its Applications 13 International Journal of Mathematical Education in Science and Technology 9 Communications in Statistics. Theory and Methods 7 Journal of Statistical Planning and Inference 6 Linear and Multilinear Algebra 6 Applied Mathematics and Computation 6 Statistics 6 Statistical Papers 5 Sankhyā. Series A. Methods and Techniques 4 Statistica 4 Acta Applicandae Mathematicae 3 Computational Statistics and Data Analysis 3 Test 3 Discussiones Mathematicae. Probability and Statistics 3 Springer-Lehrbuch 2 Computers & Mathematics with Applications 2 Scandinavian Journal of Statistics 2 Annals of the Institute of Statistical Mathematics 2 Computational Statistics Quarterly 2 Communications in Statistics. Simulation and Computation 2 Statistische Hefte 2 Methods of Operations Research 2 The College Mathematics Journal 1 American Mathematical Monthly 1 Metrika 1 The Australian Journal of Statistics 1 Biometrical Journal 1 Industrial Mathematics 1 Journal of Econometrics 1 Journal of Multivariate Analysis 1 Sankhyā. Series B. Methodological 1 Statistica Neerlandica 1 Statistics & Probability Letters 1 SIAM Journal on Matrix Analysis and Applications 1 Economics Letters 1 Acta Mathematica Universitatis Comenianae. New Series 1 Journal of Statistical Computation and Simulation 1 Tatra Mountains Mathematical Publications 1 Discussiones Mathematicae. Algebra and Stochastic Methods 1 ELA. The Electronic Journal of Linear Algebra 1 Journal of Applied Mathematics and Decision Sciences 1 Australian & New Zealand Journal of Statistics 1 Discussiones Mathematicae. General Algebra and Applications 1 Acta Universitatis Apulensis. Mathematics - Informatics 1 International Journal of Information & Systems Sciences 1 Mathematical Systems in Economics 1 Journal of the Italian Statistical Society 1 ISRN Applied Mathematics
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#### Fields

 98 Statistics (62-XX) 64 Linear and multilinear algebra; matrix theory (15-XX) 6 Combinatorics (05-XX) 5 Mathematics education (97-XX) 4 General and overarching topics; collections (00-XX) 3 Geometry (51-XX) 2 History and biography (01-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

106 Publications have been cited 844 times in 572 Documents Cited by Year
Core inverse of matrices. Zbl 1202.15009
Baksalary, Oskar Maria; Trenkler, Götz
2010
Mean squared error matrix comparisons between biased estimators - an overview of recent results. Zbl 0703.62066
Trenkler, G.; Toutenburg, H.
1990
Nonsingularity of the difference of two oblique projectors. Zbl 0946.15020
Gross, Jürgen; Trenkler, Götz
1999
Generalized and hypergeneralized projectors. Zbl 0887.15024
Groß, Jürgen; Trenkler, Götz
1997
Quasi minimax-estimation in the linear regression model. Zbl 0635.62066
Trenkler, G.; Stahlecker, P.
1987
On a generalized core inverse. Zbl 1334.15009
Baksalary, Oskar Maria; Trenkler, Götz
2014
Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Zbl 0728.15011
Baksalary, Jerzy K.; Trenkler, Götz
1991
On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. Zbl 0559.62054
Trenkler, Götz
1984
Hadamard, Khatri-Rao, Kronecker and other matrix products. Zbl 1159.15008
Liu, Shuangzhe; Trenkler, Götz
2008
Characterizations of EP, normal, and Hermitian matrices. Zbl 1151.15023
Baksalary, Oskar Maria; Trenkler, Götz
2008
On a matrix decomposition of Hartwig and Spindelböck. Zbl 1180.15004
Baksalary, Oskar Maria; Styan, George P. H.; Trenkler, Götz
2009
Mean square error matrix comparisons of estimators in linear regression. Zbl 0594.62075
Trenkler, Götz
1985
Further results on generalized and hypergeneralized projectors. Zbl 1151.15022
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Liu, Xiaoji; Trenkler, Götz
2008
Mean square error matrix improvements and admissibility of linear estimators. Zbl 0685.62052
Baksalary, Jerzy K.; Liski, Erkki P.; Trenkler, Götz
1989
Biased estimators in the linear regression model. Zbl 0471.62070
Trenkler, Götz
1981
Column space equalities for orthogonal projectors. Zbl 1169.15007
Baksalary, Oskar Maria; Trenkler, Götz
2009
Some further results on Hermitian-matrix inequalities. Zbl 0753.15014
Baksalary, Jerzy K.; Schipp, Bernhard; Trenkler, Götz
1992
Revisitation of the product of two orthogonal projectors. Zbl 1167.15018
Baksalary, Oskar Maria; Trenkler, Götz
2009
On the product of oblique projectors. Zbl 0929.15016
Groß, Jürgen; Trenkler, Götz
1998
Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Zbl 0778.62061
Stahlecker, Peter; Trenkler, Götz
1993
On disjoint range matrices. Zbl 1221.15005
Baksalary, Oskar Maria; Trenkler, Götz
2011
On angles and distances between subspaces. Zbl 1177.15024
Baksalary, Oskar Maria; Trenkler, Götz
2009
The equality of linear transforms of the ordinary least squares estimator and the best linear unbiased estimator. Zbl 1004.62056
Gross, Jürgen; Trenkler, Götz; Werner, Hans Joachim
2001
A projector oriented approach to the best linear unbiased estimator. Zbl 1247.62165
Baksalary, Oskar Maria; Trenkler, Götz
2009
A note on superiority comparisons of homogeneous linear estimators. Zbl 0523.62066
Trenkler, Götz; Trenkler, Dietrich
1983
Functions of orthogonal projectors involving the Moore-Penrose inverse. Zbl 1189.15004
Baksalary, Oskar Maria; Trenkler, Götz
2010
Characterizations of oblique and orthogonal projectors. Zbl 0827.62054
Trenkler, Götz
1994
Minimum mean square error estimation in linear regression. Zbl 0786.62068
Liski, Erkki P.; Toutenburg, Helge; Trenkler, Götz
1993
Full and partial minimax estimation in regression analysis with additional linear constraints. Zbl 0653.62053
Stahlecker, P.; Trenkler, G.
1988
Partial minimax estimation in regression analysis. Zbl 0647.62063
Hering, F.; Trenkler, G.; Stahlecker, P.
1987
Rank formulae from the perspective of orthogonal projectors. Zbl 1220.15005
Baksalary, Oskar Maria; Trenkler, Götz
2011
Eigenvalues of functions of orthogonal projectors. Zbl 1177.15010
Baksalary, Oskar Maria; Trenkler, Götz
2009
A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Zbl 1038.15001
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Trenkler, Götz
2003
On semi-orthogonality and a special class of matrices. Zbl 0949.15036
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
1999
Nonnegative minimum biased quadratic estimation in the linear regression models. Zbl 0844.62052
Gnot, S.; Trenkler, G.; Zmyślony, R.
1995
Pre-test procedures and forecasting in the regression model under restrictions. Zbl 0761.62093
Trenkler, G.; Toutenburg, H.
1992
Generalized mean squared error comparisons of biased regression estimators. Zbl 0465.62063
Trenkler, Götz
1980
Quaternions: Further contributions to a matrix oriented approach. Zbl 0981.15014
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
2001
Mean square error matrix superiority of empirical Bayes estimators under misspecification. Zbl 0839.62005
Wei, L.; Trenkler, G.
1995
On the projectors $$\mathbf F\mathbf F^\dagger$$ and $$\mathbf F^\dagger\mathbf F$$. Zbl 1222.15003
Baksalary, Oskar Maria; Trenkler, Götz
2011
On a subspace metric based on matrix rank. Zbl 1202.15026
Baksalary, Oskar Maria; Trenkler, Götz
2010
On the equality of linear statistics in General Gauss-Markov model. Zbl 1008.62631
Groß, J.; Trenkler, G.
1998
Leverage and Cochrane-Orcutt estimation in linear regression. Zbl 0784.62063
Stemann, D.; Trenkler, G.
1993
Mean square error matrix comparisons among restricted least squares estimators. Zbl 0639.62060
Trenkler, Götz
1987
Between OLSE and BLUE. Zbl 1334.62106
Baksalary, Oskar Maria; Trenkler, Götz
2011
On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006
Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz
2010
On generalized quadratic matrices. Zbl 1086.15504
Farebrother, Richard W.; Trenkler, Götz
2005
The Bayes estimator in a misspecified linear regression model. Zbl 0852.62032
Trenkler, G.; Wei, L.
1996
Linear and ellipsoidal restrictions in linear regression. Zbl 0809.62060
Stahlecker, P.; Trenkler, G.
1991
On $$k$$-potent matrices. Zbl 1283.15043
Baksalary, Oskar Maria; Trenkler, Götz
2013
Let us do the twist again. Zbl 1416.62386
Baksalary, Oskar Maria; Trenkler, Götz; Liski, Erkki
2013
On column and null spaces of functions of a pair of oblique projectors. Zbl 1277.15006
Baksalary, Oskar Maria; Trenkler, Götz
2013
Third and fourth moment matrices of vec $$X'$$ in multivariate analysis. Zbl 1009.62045
Neudecker, Heinz; Trenkler, Götz
2002
Dropping variables versus use of proxy variables in linear regression. Zbl 0849.62035
Trenkler, G.; Stahlecker, P.
1996
Mean square error matrix superiority of estimators under linear restrictions and misspecification. Zbl 1328.62452
Wijekoon, P.; Trenkler, G.
1989
Some remarks on a ridge-type-estimator and good prior means. Zbl 0696.62292
Trenkler, Götz
1988
Minimax estimation with additional linear restrictions. A simulation study. Zbl 0695.62158
Schipp, B.; Trenkler, G.; Stahlecker, P.
1988
Nichtparametrische statistische Methoden. Zbl 0369.62042
Büning, Herbert; Trenkler, Götz
1978
An alternative approach to characterize the commutativity of orthogonal projectors. Zbl 1155.15017
Baksalary, Oskar Maria; Trenkler, Götz
2008
The Moore-Penrose inverse of a semi-magic square is semi-magic. Zbl 1012.15005
Schmidt, Karsten; Trenkler, Götz
2001
Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Zbl 0981.62047
Groß, Jürgen; Trenkler, Götz; Liski, Erkki P.
1998
Estimation from transformed data under the linear regression model. Zbl 0885.62080
Liski, Erkki P.; Trenkler, Götz; Groß, Jürgen
1997
Nonparametric statistical methods. 2., erw. u. völlig überarb. Aufl. Zbl 0820.62031
Büning, Herbert; Trenkler, Götz
1994
A note on comparing stochastically restricted linear estimators in a regression model. Zbl 0804.62062
Trenkler, Götz
1993
Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Zbl 0825.62571
Toutenberg, H.; Trenkler, G.
1990
Mean square error matrix superiority of the mixed regression estimator under misspecification. Zbl 0718.62153
Trenkler, Götz; Wijekoon, Pushba
1989
A simulation study comparing some biased estimators in the linear model. Zbl 0612.62096
Trenkler, D.; Trenkler, G.
1984
On a pair of vector spaces. Zbl 1292.15002
Baksalary, Oskar Maria; Trenkler, Götz
2013
Subsets and subspaces. Zbl 1188.15002
Baksalary, Oskar Maria; Trenkler, Götz
2010
Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Zbl 1102.62059
Neudecker, Heinz; Trenkler, Götz
2005
A multivariate version of Samuelson’s inequality. Zbl 1123.62048
Trenkler, Götz; Puntanen, Simo
2005
When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide? Zbl 0884.62070
Groß, Jürgen; Trenkler, Götz
1997
Records tests for trend in location. Zbl 0897.62044
Diersen, J.; Trenkler, G.
1996
Minimax adjustment technique in a parameter restricted linear model. Zbl 0844.62059
Stahlecker, Peter; Knautz, Henning; Trenkler, Götz
1996
Singular magic squares. Zbl 0827.15003
Trenkler, Götz
1994
Minimum mean square error ridge estimation. Zbl 0569.62059
Trenkler, Dietrich; Trenkler, Götz
1984
On the entries of orthogonal projection matrices. Zbl 1266.15048
Baksalary, Oskar Maria; Trenkler, Götz
2013
A simple metric for finite dimensional vector spaces. Zbl 1313.15002
Baksalary, Oskar Maria; Trenkler, Götz
2012
Eigenspaces of the proper rotation matrices. Zbl 1292.97033
Baksalary, Oskar Maria; Trenkler, Götz
2010
Further inequalities involving the Khatri-Rao product. Zbl 1179.15022
Yang, Zhongpeng; Liu, Shuangzhe; Trenkler, Götz
2009
The Sherman-Morrison formula and eigenvalues of a special bordered matrix. Zbl 1164.15317
Trenkler, G.; Trenkler, D.
2005
Matrices which take a given vector into a given vector – revisited. Zbl 1047.15003
Trenkler, Götz
2004
The Moore-Penrose inverse and the vector product. Zbl 1012.15004
Trenkler, Götz
2002
On the efficiency of the Cochrane-Orcutt estimator in the serially correlated error components regression model for panel data. Zbl 1009.62555
Song, Seuck Heun; Trenkler, Götz
2001
The vector cross product from an algebraic point of view. Zbl 0999.15033
Trenkler, Götz
2001
Some further results on the efficiency of the Cochrane-Orcutt-estimator. Zbl 0951.62057
Stemann, D.; Trenkler, G.
2000
On properties of $$3\times 3$$ semi-magic squares. Zbl 1017.05028
Gross, J.; Troschke, S.-O.; Trenkler, G.
1999
The vector cross product in $$\mathbb{C}^3$$. Zbl 1018.15027
Gross, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
1999
On the eigenvalues of $$3\times 3$$ magic squares. Zbl 1017.05029
Trenkler, Götz
1999
Vector equations and their solutions. Zbl 1025.15002
Trenkler, Götz
1998
Using first differences as a device against multicollinearity. Zbl 0936.91054
Toutenburg, Helge; Trenkler, Götz
1998
Modern matrix algebra. With applications to statistics. Zbl 0897.15002
Schmidt, Karsten; Trenkler, Götz
1998
On the equality of usual and Amemiya’s partially generalized least squares estimator. Zbl 0954.62547
Groß, Jürgen; Trenkler, Götz
1997
Nonnegative quadratic estimation of the mean squared errors of minimax estimators in the linear regression model. Zbl 0844.62053
Gnot, S.; Trenkler, G.
1996
On the least squares distance between affine subspaces. Zbl 0852.15003
Gross, Jürgen; Trenkler, Götz
1996
An objective stability criterion for selecting the biasing parameter from the ridge trace. Zbl 0861.62056
Trenkler, Dietrich; Trenkler, Götz
1995
Some bounds for bias and variance of $$S^ 2$$ under dependence. Zbl 0819.62019
Knautz, Henning; Trenkler, Götz
1995
Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Zbl 0809.62056
Gnot, Stanisław; Knautz, Henning; Trenkler, Götz
1994
Pre-test estimation in the linear regression model with competing restrictions. Zbl 0804.62060
Pordzik, Pawel R.; Trenkler, Götz
1994
A note on the correlation between $$S^ 2$$ and the least squares estimator in the linear regression model. Zbl 0774.62070
Knautz, H.; Trenkler, G.
1993
On a generalized core inverse. Zbl 1334.15009
Baksalary, Oskar Maria; Trenkler, Götz
2014
On $$k$$-potent matrices. Zbl 1283.15043
Baksalary, Oskar Maria; Trenkler, Götz
2013
Let us do the twist again. Zbl 1416.62386
Baksalary, Oskar Maria; Trenkler, Götz; Liski, Erkki
2013
On column and null spaces of functions of a pair of oblique projectors. Zbl 1277.15006
Baksalary, Oskar Maria; Trenkler, Götz
2013
On a pair of vector spaces. Zbl 1292.15002
Baksalary, Oskar Maria; Trenkler, Götz
2013
On the entries of orthogonal projection matrices. Zbl 1266.15048
Baksalary, Oskar Maria; Trenkler, Götz
2013
A simple metric for finite dimensional vector spaces. Zbl 1313.15002
Baksalary, Oskar Maria; Trenkler, Götz
2012
On disjoint range matrices. Zbl 1221.15005
Baksalary, Oskar Maria; Trenkler, Götz
2011
Rank formulae from the perspective of orthogonal projectors. Zbl 1220.15005
Baksalary, Oskar Maria; Trenkler, Götz
2011
On the projectors $$\mathbf F\mathbf F^\dagger$$ and $$\mathbf F^\dagger\mathbf F$$. Zbl 1222.15003
Baksalary, Oskar Maria; Trenkler, Götz
2011
Between OLSE and BLUE. Zbl 1334.62106
Baksalary, Oskar Maria; Trenkler, Götz
2011
Core inverse of matrices. Zbl 1202.15009
Baksalary, Oskar Maria; Trenkler, Götz
2010
Functions of orthogonal projectors involving the Moore-Penrose inverse. Zbl 1189.15004
Baksalary, Oskar Maria; Trenkler, Götz
2010
On a subspace metric based on matrix rank. Zbl 1202.15026
Baksalary, Oskar Maria; Trenkler, Götz
2010
On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006
Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz
2010
Subsets and subspaces. Zbl 1188.15002
Baksalary, Oskar Maria; Trenkler, Götz
2010
Eigenspaces of the proper rotation matrices. Zbl 1292.97033
Baksalary, Oskar Maria; Trenkler, Götz
2010
On a matrix decomposition of Hartwig and Spindelböck. Zbl 1180.15004
Baksalary, Oskar Maria; Styan, George P. H.; Trenkler, Götz
2009
Column space equalities for orthogonal projectors. Zbl 1169.15007
Baksalary, Oskar Maria; Trenkler, Götz
2009
Revisitation of the product of two orthogonal projectors. Zbl 1167.15018
Baksalary, Oskar Maria; Trenkler, Götz
2009
On angles and distances between subspaces. Zbl 1177.15024
Baksalary, Oskar Maria; Trenkler, Götz
2009
A projector oriented approach to the best linear unbiased estimator. Zbl 1247.62165
Baksalary, Oskar Maria; Trenkler, Götz
2009
Eigenvalues of functions of orthogonal projectors. Zbl 1177.15010
Baksalary, Oskar Maria; Trenkler, Götz
2009
Further inequalities involving the Khatri-Rao product. Zbl 1179.15022
Yang, Zhongpeng; Liu, Shuangzhe; Trenkler, Götz
2009
Hadamard, Khatri-Rao, Kronecker and other matrix products. Zbl 1159.15008
Liu, Shuangzhe; Trenkler, Götz
2008
Characterizations of EP, normal, and Hermitian matrices. Zbl 1151.15023
Baksalary, Oskar Maria; Trenkler, Götz
2008
Further results on generalized and hypergeneralized projectors. Zbl 1151.15022
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Liu, Xiaoji; Trenkler, Götz
2008
An alternative approach to characterize the commutativity of orthogonal projectors. Zbl 1155.15017
Baksalary, Oskar Maria; Trenkler, Götz
2008
On generalized quadratic matrices. Zbl 1086.15504
Farebrother, Richard W.; Trenkler, Götz
2005
Estimation of the Kronecker and products of two mean vectors in multivariate analysis. Zbl 1102.62059
Neudecker, Heinz; Trenkler, Götz
2005
A multivariate version of Samuelson’s inequality. Zbl 1123.62048
Trenkler, Götz; Puntanen, Simo
2005
The Sherman-Morrison formula and eigenvalues of a special bordered matrix. Zbl 1164.15317
Trenkler, G.; Trenkler, D.
2005
Matrices which take a given vector into a given vector – revisited. Zbl 1047.15003
Trenkler, Götz
2004
A revisitation of formulae for the Moore-Penrose inverse of modified matrices. Zbl 1038.15001
Baksalary, Jerzy K.; Baksalary, Oskar Maria; Trenkler, Götz
2003
Third and fourth moment matrices of vec $$X'$$ in multivariate analysis. Zbl 1009.62045
Neudecker, Heinz; Trenkler, Götz
2002
The Moore-Penrose inverse and the vector product. Zbl 1012.15004
Trenkler, Götz
2002
The equality of linear transforms of the ordinary least squares estimator and the best linear unbiased estimator. Zbl 1004.62056
Gross, Jürgen; Trenkler, Götz; Werner, Hans Joachim
2001
Quaternions: Further contributions to a matrix oriented approach. Zbl 0981.15014
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
2001
The Moore-Penrose inverse of a semi-magic square is semi-magic. Zbl 1012.15005
Schmidt, Karsten; Trenkler, Götz
2001
On the efficiency of the Cochrane-Orcutt estimator in the serially correlated error components regression model for panel data. Zbl 1009.62555
Song, Seuck Heun; Trenkler, Götz
2001
The vector cross product from an algebraic point of view. Zbl 0999.15033
Trenkler, Götz
2001
Some further results on the efficiency of the Cochrane-Orcutt-estimator. Zbl 0951.62057
Stemann, D.; Trenkler, G.
2000
Nonsingularity of the difference of two oblique projectors. Zbl 0946.15020
Gross, Jürgen; Trenkler, Götz
1999
On semi-orthogonality and a special class of matrices. Zbl 0949.15036
Groß, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
1999
On properties of $$3\times 3$$ semi-magic squares. Zbl 1017.05028
Gross, J.; Troschke, S.-O.; Trenkler, G.
1999
The vector cross product in $$\mathbb{C}^3$$. Zbl 1018.15027
Gross, Jürgen; Trenkler, Götz; Troschke, Sven-Oliver
1999
On the eigenvalues of $$3\times 3$$ magic squares. Zbl 1017.05029
Trenkler, Götz
1999
On the product of oblique projectors. Zbl 0929.15016
Groß, Jürgen; Trenkler, Götz
1998
On the equality of linear statistics in General Gauss-Markov model. Zbl 1008.62631
Groß, J.; Trenkler, G.
1998
Necessary and sufficient conditions for superiority of misspecified restricted least squares regression estimator. Zbl 0981.62047
Groß, Jürgen; Trenkler, Götz; Liski, Erkki P.
1998
Vector equations and their solutions. Zbl 1025.15002
Trenkler, Götz
1998
Using first differences as a device against multicollinearity. Zbl 0936.91054
Toutenburg, Helge; Trenkler, Götz
1998
Modern matrix algebra. With applications to statistics. Zbl 0897.15002
Schmidt, Karsten; Trenkler, Götz
1998
Generalized and hypergeneralized projectors. Zbl 0887.15024
Groß, Jürgen; Trenkler, Götz
1997
Estimation from transformed data under the linear regression model. Zbl 0885.62080
Liski, Erkki P.; Trenkler, Götz; Groß, Jürgen
1997
When do linear transforms of ordinary least squares and Gauss-Markov estimator coincide? Zbl 0884.62070
Groß, Jürgen; Trenkler, Götz
1997
On the equality of usual and Amemiya’s partially generalized least squares estimator. Zbl 0954.62547
Groß, Jürgen; Trenkler, Götz
1997
The Bayes estimator in a misspecified linear regression model. Zbl 0852.62032
Trenkler, G.; Wei, L.
1996
Dropping variables versus use of proxy variables in linear regression. Zbl 0849.62035
Trenkler, G.; Stahlecker, P.
1996
Records tests for trend in location. Zbl 0897.62044
Diersen, J.; Trenkler, G.
1996
Minimax adjustment technique in a parameter restricted linear model. Zbl 0844.62059
Stahlecker, Peter; Knautz, Henning; Trenkler, Götz
1996
Nonnegative quadratic estimation of the mean squared errors of minimax estimators in the linear regression model. Zbl 0844.62053
Gnot, S.; Trenkler, G.
1996
On the least squares distance between affine subspaces. Zbl 0852.15003
Gross, Jürgen; Trenkler, Götz
1996
Nonnegative minimum biased quadratic estimation in the linear regression models. Zbl 0844.62052
Gnot, S.; Trenkler, G.; Zmyślony, R.
1995
Mean square error matrix superiority of empirical Bayes estimators under misspecification. Zbl 0839.62005
Wei, L.; Trenkler, G.
1995
An objective stability criterion for selecting the biasing parameter from the ridge trace. Zbl 0861.62056
Trenkler, Dietrich; Trenkler, Götz
1995
Some bounds for bias and variance of $$S^ 2$$ under dependence. Zbl 0819.62019
Knautz, Henning; Trenkler, Götz
1995
Characterizations of oblique and orthogonal projectors. Zbl 0827.62054
Trenkler, Götz
1994
Nonparametric statistical methods. 2., erw. u. völlig überarb. Aufl. Zbl 0820.62031
Büning, Herbert; Trenkler, Götz
1994
Singular magic squares. Zbl 0827.15003
Trenkler, Götz
1994
Using nonnegative minimum biased quadratic estimation for variable selection in the linear regression model. Zbl 0809.62056
Gnot, Stanisław; Knautz, Henning; Trenkler, Götz
1994
Pre-test estimation in the linear regression model with competing restrictions. Zbl 0804.62060
Pordzik, Pawel R.; Trenkler, Götz
1994
Minimax estimation in linear regression with singular covariance structure and convex polyhedral constraints. Zbl 0778.62061
Stahlecker, Peter; Trenkler, Götz
1993
Minimum mean square error estimation in linear regression. Zbl 0786.62068
Liski, Erkki P.; Toutenburg, Helge; Trenkler, Götz
1993
Leverage and Cochrane-Orcutt estimation in linear regression. Zbl 0784.62063
Stemann, D.; Trenkler, G.
1993
A note on comparing stochastically restricted linear estimators in a regression model. Zbl 0804.62062
Trenkler, Götz
1993
A note on the correlation between $$S^ 2$$ and the least squares estimator in the linear regression model. Zbl 0774.62070
Knautz, H.; Trenkler, G.
1993
Some further results on Hermitian-matrix inequalities. Zbl 0753.15014
Baksalary, Jerzy K.; Schipp, Bernhard; Trenkler, Götz
1992
Pre-test procedures and forecasting in the regression model under restrictions. Zbl 0761.62093
Trenkler, G.; Toutenburg, H.
1992
Pre-test estimation in the linear regression model with competing linear constraints. Zbl 0770.62052
Hessenius, Helga; Trenkler, Götz
1992
Nonnegative and positive definiteness of matrices modified by two matrices of rank one. Zbl 0728.15011
Baksalary, Jerzy K.; Trenkler, Götz
1991
Linear and ellipsoidal restrictions in linear regression. Zbl 0809.62060
Stahlecker, P.; Trenkler, G.
1991
Covariance adjustment in biased estimation. Zbl 0870.62042
Baksalary, Jerzy K.; Trenkler, Götz
1991
Mean square error matrix comparisons between biased restricted least squares estimators. Zbl 0746.62065
Trenkler, Götz
1991
Mean squared error matrix comparisons between biased estimators - an overview of recent results. Zbl 0703.62066
Trenkler, G.; Toutenburg, H.
1990
Mean square error matrix comparisons of optimal and classical predictors and estimators in linear regression. Zbl 0825.62571
Toutenberg, H.; Trenkler, G.
1990
Mean square error matrix improvements and admissibility of linear estimators. Zbl 0685.62052
Baksalary, Jerzy K.; Liski, Erkki P.; Trenkler, Götz
1989
Mean square error matrix superiority of estimators under linear restrictions and misspecification. Zbl 1328.62452
Wijekoon, P.; Trenkler, G.
1989
Mean square error matrix superiority of the mixed regression estimator under misspecification. Zbl 0718.62153
Trenkler, Götz; Wijekoon, Pushba
1989
Full and partial minimax estimation in regression analysis with additional linear constraints. Zbl 0653.62053
Stahlecker, P.; Trenkler, G.
1988
Some remarks on a ridge-type-estimator and good prior means. Zbl 0696.62292
Trenkler, Götz
1988
Minimax estimation with additional linear restrictions. A simulation study. Zbl 0695.62158
Schipp, B.; Trenkler, G.; Stahlecker, P.
1988
Quasi minimax-estimation in the linear regression model. Zbl 0635.62066
Trenkler, G.; Stahlecker, P.
1987
Partial minimax estimation in regression analysis. Zbl 0647.62063
Hering, F.; Trenkler, G.; Stahlecker, P.
1987
Mean square error matrix comparisons among restricted least squares estimators. Zbl 0639.62060
Trenkler, Götz
1987
Mean square error matrix comparisons between mixed estimators. Zbl 0626.62052
Freund, E.; Trenkler, G.
1986
Mean square error matrix comparisons of estimators in linear regression. Zbl 0594.62075
Trenkler, Götz
1985
On the performance of biased estimators in the linear regression model with correlated or heteroscedastic errors. Zbl 0559.62054
Trenkler, Götz
1984
A simulation study comparing some biased estimators in the linear model. Zbl 0612.62096
Trenkler, D.; Trenkler, G.
1984
Minimum mean square error ridge estimation. Zbl 0569.62059
Trenkler, Dietrich; Trenkler, Götz
1984
...and 6 more Documents
all top 5

#### Cited by 495 Authors

 64 Trenkler, Götz 36 Chen, Jianlong 35 Mosić, Dijana 33 Baksalary, Oskar Maria 23 Stahlecker, Peter 21 Thome, Néstor 20 Benítez Lopez, Julio 18 Gross, Jürgen 18 Liu, Xiaoji 18 Tian, Yongge 17 Yang, Hu 14 Baksalary, Jerzy K. 13 Deng, Chunyuan 12 Özkale, M. Revan 12 Puntanen, Simo 11 Đorđević, Dragan S. 11 Xu, Sanzhang 10 Kaçıranlar, Selahattin 10 Liski, Erkki P. 10 Wei, Laisheng 9 Li, Tingting 9 Ma, Haifeng 9 Patrício, Pedro 9 Wang, Hongxing 9 Wei, Yimin 9 Zhou, Mengmeng 8 Cvetković-Ilić, Dragana S. 8 Gao, Yuefeng 8 Markiewicz, Augustyn 8 Ohtani, Kazuhiro 8 Toutenburg, Helge 7 Özdemir, Halim 7 Rakočević, Vladimir 7 Stanimirović, Predrag S. 6 Akdeniz, Fikri 6 Arnold, Bernhard F. 6 Li, Yalian 6 Rakić, Dragan S. 6 Schipp, Bernhard 6 Styan, George P. H. 6 Wijekoon, Pushpakanthie 6 Zhu, Huihui 5 Ferreyra, David E. 5 Koliha, Jerry J. 5 Kyrchei, Ivan I. 5 Schmidt, Karsten 5 Zuo, Kezheng 4 Açar, Tuğba Söküt 4 Arumairajan, Sivarajah 4 Corach, Gustavo 4 Hauke, Jan 4 Lebtahi, Leila 4 Levis, Fabián Eduardo 4 Liu, Shuangzhe 4 Malik, Saroj B. 4 Sakallioglu, Sadullah 4 Trenkler, Dietrich 4 Zhang, WeiPing 3 Chang, Xinfeng 3 Dawoud, Issam 3 Du, Hongke 3 Hurley, Ted 3 Isotalo, Jarkko 3 Jiang, Bo 3 Kala, Radosław 3 Knautz, Henning 3 Lauterbach, Jörg 3 Liu, Xuqing 3 Lone, Mohd Saleem 3 Marovt, Janko 3 Matvejchuk, Marjan Stepanovich 3 Roozbeh, Mahdi 3 Sivakumar, Koratti Chengalrayan 3 Sun, Yuqin 3 Troschke, Sven-Oliver 3 Wang, Dingguo 3 Wang, Long 3 Wencheko, Eshetu 3 Wilczyński, Maciej 3 Wu, Jibo 3 Zou, Honglin 2 Akay, Kadri Ulaş 2 Alkhamisi, Mahdi A. 2 Aslam, Muhammad Nauman 2 Behera, Ratikanta 2 Bikchentaev, Aĭrat Midkhatovich 2 Boasso, Enrico 2 Büning, Herbert 2 Calussi, Gabriele 2 Catral, Minerva 2 Chandra, Shalini 2 Chen, Jiahua 2 Chen, Ling 2 Chen, Yu 2 Clark, Todd E. 2 Coll, Carmen 2 Dinčić, Nebojša Č. 2 Djikić, Marko S. 2 Dolinar, Gregor 2 Drygas, Hilmar ...and 395 more Authors
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#### Cited in 113 Serials

 92 Linear Algebra and its Applications 58 Linear and Multilinear Algebra 47 Statistical Papers 45 Communications in Statistics. Theory and Methods 29 Applied Mathematics and Computation 26 Journal of Statistical Planning and Inference 13 Statistics & Probability Letters 13 Communications in Statistics. Simulation and Computation 12 Acta Applicandae Mathematicae 12 Statistics 11 Journal of Statistical Computation and Simulation 11 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 Communications in Algebra 6 Journal of Multivariate Analysis 6 Computational Statistics and Data Analysis 6 Frontiers of Mathematics in China 5 International Journal of Mathematical Education in Science and Technology 5 Quaestiones Mathematicae 5 Aequationes Mathematicae 5 Advances in Applied Clifford Algebras 5 Journal of Algebra and its Applications 5 Journal of Mathematics 4 Computers & Mathematics with Applications 4 Indian Journal of Pure & Applied Mathematics 4 Metrika 4 Journal of Econometrics 4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 4 Mediterranean Journal of Mathematics 4 Banach Journal of Mathematical Analysis 3 Journal of Mathematical Analysis and Applications 3 Journal of Computational and Applied Mathematics 3 Results in Mathematics 3 Acta Mathematicae Applicatae Sinica. English Series 3 Statistische Hefte 3 Test 3 Computational and Applied Mathematics 3 ELA. The Electronic Journal of Linear Algebra 3 Lobachevskii Journal of Mathematics 3 Special Matrices 3 Open Mathematics 2 Ukrainian Mathematical Journal 2 Automatica 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 SIAM Journal on Matrix Analysis and Applications 2 Economics Letters 2 Wuhan University Journal of Natural Sciences (WUJNS) 2 Journal of Applied Statistics 2 Statistical Methods and Applications 2 International Journal of Group Theory 2 Communications in Mathematics and Statistics 2 Journal of Linear and Topological Algebra 1 American Mathematical Monthly 1 Discrete Mathematics 1 International Journal of Theoretical Physics 1 Journal of Mathematical Physics 1 Psychometrika 1 Scandinavian Journal of Statistics 1 Chaos, Solitons and Fractals 1 Beiträge zur Algebra und Geometrie 1 Annals of the Institute of Statistical Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 Biometrical Journal 1 Calcolo 1 Collectanea Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Algebra 1 Proceedings of the American Mathematical Society 1 Statistica Neerlandica 1 Bulletin of the Korean Mathematical Society 1 Chinese Annals of Mathematics. Series B 1 Bulletin of the Iranian Mathematical Society 1 American Journal of Mathematical and Management Sciences 1 Physica D 1 Facta Universitatis. Series Mathematics and Informatics 1 Machine Learning 1 Neural Computation 1 Computational Statistics 1 Computational Mathematics and Mathematical Physics 1 YUJOR. Yugoslav Journal of Operations Research 1 European Journal of Operational Research 1 Glasnik Matematički. Serija III 1 Russian Mathematics 1 Computational Optimization and Applications 1 Numerical Linear Algebra with Applications 1 Turkish Journal of Mathematics 1 Advances in Computational Mathematics 1 Mathematical Communications 1 Abstract and Applied Analysis 1 Positivity 1 Journal of Inequalities and Applications 1 Australian & New Zealand Journal of Statistics 1 Data Mining and Knowledge Discovery 1 Acta Mathematica Sinica. English Series 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics 1 Central European Journal of Mathematics 1 Statistical Methods in Medical Research 1 International Journal of Wavelets, Multiresolution and Information Processing ...and 13 more Serials
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#### Cited in 37 Fields

 266 Linear and multilinear algebra; matrix theory (15-XX) 261 Statistics (62-XX) 58 Operator theory (47-XX) 50 Associative rings and algebras (16-XX) 39 Numerical analysis (65-XX) 26 Functional analysis (46-XX) 20 Order, lattices, ordered algebraic structures (06-XX) 9 Computer science (68-XX) 6 Probability theory and stochastic processes (60-XX) 6 Operations research, mathematical programming (90-XX) 5 Quantum theory (81-XX) 5 Systems theory; control (93-XX) 4 Number theory (11-XX) 3 Mathematical logic and foundations (03-XX) 3 Algebraic geometry (14-XX) 3 Category theory; homological algebra (18-XX) 3 Group theory and generalizations (20-XX) 3 Ordinary differential equations (34-XX) 3 Geometry (51-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Difference and functional equations (39-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Differential geometry (53-XX)

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