Stahlecker, Peter; Knautz, Henning; Trenkler, Götz Minimax adjustment technique in a parameter restricted linear model. (English) Zbl 0844.62059 Acta Appl. Math. 43, No. 1, 139-144 (1996). Summary: We consider an approach yielding a minimax estimator in the linear regression model with a priori information on the parameter vector, e.g., ellipsoidal restrictions. This estimator is computed directly from the loss function and can be motivated by the general Pitman nearness criterion. It turns out that this approach coincides with the projection estimator which is obtained by projecting an initial arbitrary estimate on the subset defined by the restrictions. Cited in 2 Documents MSC: 62J05 Linear regression; mixed models 62C20 Minimax procedures in statistical decision theory Keywords:minimax adjustment; minimax estimator; a priori information; ellipsoidal restrictions; loss function; Pitman nearness criterion; projection estimator PDFBibTeX XMLCite \textit{P. Stahlecker} et al., Acta Appl. Math. 43, No. 1, 139--144 (1996; Zbl 0844.62059) Full Text: DOI References: [1] Fountain R. L.: 1991, Pitman closeness comparison of linear estimators: A canonical form,Comm. Statist. Theory Methods 20(11), 3535-3550. · Zbl 0800.62276 · doi:10.1080/03610929108830723 [2] Peddada S. D. and Khattree R.: 1986, OnPitman nearness and variance of estimators,Comm. Statist. Theory Methods 15(10), 3005-3017. · Zbl 0615.62030 · doi:10.1080/03610928608829292 [3] Pilz J.: 1991,Bayesian Estimation and Experimental Design in Linear Regression Models, 2nd edn, Wiley, New York. · Zbl 0745.62068 [4] Pitman E. J. G.: 1937, The closest estimates of statistical parameters,Proc. Cambridge Philosoph. Soc. 33, 212-222. · JFM 63.0515.03 · doi:10.1017/S0305004100019563 [5] Rothenberg T. J.: 1973,Efficient Estimation with A Priori Information, Yale University Press, New Haven. · Zbl 0291.62141 [6] Schmidt K. and Stahlecker P.: 1995, Reducing maximum risk of regression estimators by polyhedral projection,J. Statist. Comput. 52, 1-15. · Zbl 0842.62056 · doi:10.1080/00949659508811648 [7] Stahlecker P.: 1987,A priori Information und Minimax-Schätzung im linearen Regressionsmodell, Mathematical Systems in Economics 108, Verlag Athenäum, Frankfurt-am-Main. · Zbl 0651.62106 [8] Stahlecker P. and Trenkler G.: 1993, Minimax estimation in linear regression with singular covariance structure and polyhedral constraints,J. Statist. Plann. Inference 36, 185-196. · Zbl 0778.62061 · doi:10.1016/0378-3758(93)90123-N This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.