×

Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions. (English) Zbl 1368.62196

Summary: The local influence method has proven to be a useful and powerful tool for detecting influential observations on the estimation of model parameters. This method has been widely applied in different studies related to econometric and statistical modelling. We propose a methodology based on the Lagrange multiplier method with a linear penalty function to assess local influence in the possibly heteroskedastic linear regression model with exact restrictions. The restricted maximum likelihood estimators and information matrices are presented for the postulated model. Several perturbation schemes for the local influence method are investigated to identify potentially influential observations. Three real-world examples are included to illustrate and validate our methodology.

MSC:

62J05 Linear regression; mixed models
62J20 Diagnostics, and linear inference and regression

Software:

AER
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Atkinson AC, Riani M (2000) Robust diagnostic regression analysis. Springer, Berlin · Zbl 0964.62063 · doi:10.1007/978-1-4612-1160-0
[2] Atkinson AC, Riani M, Cerioli A (2004) Exploring multivariate data with the forward search. Springer, Berlin · Zbl 1049.62057 · doi:10.1007/978-0-387-21840-3
[3] Barros M, Galea M, González M, Leiva V (2010) Influence diagnostics in the tobit censored response model. Stat Methods Appl 19:379-397 · Zbl 1332.62382 · doi:10.1007/s10260-010-0135-y
[4] Billor N, Loynes RM (1993) Local influence: a new approach. Commun Stat Theory Methods 22:1595-1611 · Zbl 0792.62060 · doi:10.1080/03610929308831105
[5] Billor N, Loynes RM (1999) An application of the local influence approach to ridge regression. J Appl Stat 2:177-183 · Zbl 1072.62608 · doi:10.1080/02664769922511
[6] Chatterjee S, Hadi AS (1988) Sensitivity analysis in linear regression. Wiley, New York · Zbl 0648.62066 · doi:10.1002/9780470316764
[7] Cook D (1986) Assessment of local influence. J R Stat Soc B 48:133-169 · Zbl 0608.62041
[8] Chipman JS, Rao MM (1964) The treatment of linear restrictions in regression analysis. Econometrica 32:198-209 · Zbl 0143.43305 · doi:10.2307/1913745
[9] Cook D, Weisberg S (1982) Residuals and influence in regression. Chapman & Hall, New York · Zbl 0564.62054
[10] Cysneiros FJA, Paula GA (2005) Restricted methods in symmetrical linear regression models. Comput Stat Data Anal 49:689-708 · Zbl 1429.62285 · doi:10.1016/j.csda.2004.06.001
[11] de Castro M, Galea M, Bolfarine H (2007) Local influence assessment in heteroscedastic measurement error models. Comput Stat Data Anal 52:1132-1142 · Zbl 1452.62494 · doi:10.1016/j.csda.2007.05.012
[12] Díaz-García JA, Galea M, Leiva V (2003) Influence diagnostics for multivariate elliptic regression linear models. Commun Stat Theory Methods 32:625-641 · Zbl 1029.62067 · doi:10.1081/STA-120018555
[13] Efron B, Hinkley D (1978) Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika 65:457-487 · Zbl 0401.62002 · doi:10.1093/biomet/65.3.457
[14] Galea M, de Castro M (2012) Influence assessment in an heteroscedastic errors-in-variables model. Commun Stat Theory Methods 41:1350-1363 · Zbl 1319.62152 · doi:10.1080/03610926.2010.543301
[15] Galea M, Diaz-Garcia JA, Vilca F (2008) Influence diagnostics in the capital asset pricing model under elliptical distributions. J Appl Stat 35:179-192 · Zbl 1516.62291 · doi:10.1080/02664760701775712
[16] Galea M, Paula GA, Bolfarine H (1997) Local influence for elliptical linear models. J R Stat Soc D 46:71-79 · doi:10.1111/1467-9884.00060
[17] Greene WH (2007) Econometric analysis. Prentice Hall, New York
[18] Gross J (2003) Linear regression. Springer, Berlin · Zbl 1039.62061 · doi:10.1007/978-3-642-55864-1
[19] Hocking R (2003) Methods and applications of linear models: regression and the analysis of variance. Wiley, New York · Zbl 1038.62059 · doi:10.1002/0471434159
[20] Judge GG, Hill RC, Griffiths WE, Lutkepohl H, Lee TC (1988) Introduction to the theory and practice of econometrics. Wiley, New York · Zbl 0731.62155
[21] Kleiber C, Zeileis A (2008) Applied econometrics with R. Springer, Berlin · Zbl 1155.91004 · doi:10.1007/978-0-387-77318-6
[22] Leiva V, Barros M, Paula GA, Galea M (2007) Influence diagnostics in log-Birnbaum-Saunders regression models with censored data. Comput Stat Data Anal 51:5694-5707 · Zbl 1445.62199 · doi:10.1016/j.csda.2006.09.020
[23] Leiva V, Rojas E, Galea M, Sanhueza A (2014) Diagnostics in Birnbaum-Saunders accelerated life models with an application to fatigue data. Appl Stoch Model Bus Ind 30:115-131 · doi:10.1002/asmb.1944
[24] Liu S (2000) On local influence for elliptical linear models. Stat Papers 41:211-224 · Zbl 0948.62054 · doi:10.1007/BF02926104
[25] Liu S (2002) Local influence in multivariate elliptical linear regression models. Linear Algebra Appl 354:211-224
[26] Liu S (2004) On diagnostics in conditionally heteroskedastic time series models under elliptical distributions. J Appl Prob 41A:393-405 · Zbl 1049.62100 · doi:10.1239/jap/1082552214
[27] Liu S, Ahmed SE, Ma LY (2009) Influence diagnostics in the linear regression model with linear stochastic restrictions. Pak J Stat 25:647-662 · Zbl 1509.62286
[28] Liu S, Ma T, Polasek W (2014) Spatial system estimators for panel models: a sensitivity and simulation study. Math Comput Simul 101:78-102 · Zbl 07312605 · doi:10.1016/j.matcom.2014.03.003
[29] Liu S, Neudecker H (2007) Local sensitivity of the restricted least squares estimator in the linear model. Stat Papers 48:525-525 · doi:10.1007/s00362-006-0354-3
[30] Magnus JR, Neudecker H (1999) Matrix differential calculus with applications in statistics and econometrics. Wiley, Chichester · Zbl 0912.15003
[31] Neudecker H, Liu S, Polasek W (1995) The hadamard product and some of its applications in statistics. Statistics 26:365-373 · Zbl 0837.62052 · doi:10.1080/02331889508802503
[32] Paula GA (1993) Assessing local influence in restricted regression models. Comput Stat Data Anal 16:63-79 · Zbl 0875.62357 · doi:10.1016/0167-9473(93)90245-O
[33] Paula GA, Cysneiros FJA (2010) Local influence under parameter constraints. Commun Stat Theory Methods 39:1212-1228 · Zbl 1188.62209 · doi:10.1080/03610920902871438
[34] Paula GA, Leiva V, Barros M, Liu S (2012) Robust statistical modeling using the Birnbaum-Saunders-\[t\] t distribution applied to insurance. Appl Stoch Models Bus Ind 28:16-34 · Zbl 06292429 · doi:10.1002/asmb.887
[35] Poon WY, Poon YS (1999) Conformal normal curvature and assessment of local influence. J R Stat Soc B 61:51-61 · Zbl 0913.62062 · doi:10.1111/1467-9868.00162
[36] Rao CR, Toutenburg H, Shalabh, Heumann C (2008) Linear models and generalizations. Springer, Berlin · Zbl 1151.62063
[37] Ramanathan R (1993) Statistical methods in econometrics. Wiley, New York
[38] Shi L, Chen G (2008) Local influence in multilevel models. Can J Stat 36:259-275 · Zbl 1144.62053 · doi:10.1002/cjs.5550360206
[39] Shi L, Huang M (2011) Stepwise local influence analysis. Comput Stat Data Anal 55:973-982 · Zbl 1284.62064 · doi:10.1016/j.csda.2010.08.001
[40] Trenkler G (1987) Mean square error matrix comparisons among restricted least squares estimators. Sankyhā A 49:96-104 · Zbl 0639.62060
[41] Wooldridge JM (2013) Introductory econometrics: a modern approach. South-Western Cengage Learning, Mason, OH
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.