TY - JOUR
T1 - On some heteroskedasticity-robust estimators of variance-covariance matrix of the least-squares estimators
AU - Bera, Anil K.
AU - Suprayitno, Totok
AU - Premaratne, Gamini
N1 - Funding Information:
We would like to thank the editor-in-chief Jagdish Srivastava and two anonymous referees for many pertinent comments that helped us to improve the paper. Thanks are also due to Roger Koenker and Paul Newbold for helpful comments on an earlier version of this paper, and Sungsup Ra for research assistance. We, however, retain the responsibility for any remaining errors. Financial support from the Research Board of the University of Illinois at Urbana-Champaign and the Office of Research, College of Commerce and Business Administration, University of Illinois at Urbana-Champaign are gratefully acknowledged.
PY - 2002/11/1
Y1 - 2002/11/1
N2 - Chesher and Jewitt (Econometrica 55 (1987) 1217) demonstrated that the Eicker (Ann. Math. Statist. 34 (1963) 447) and White (Econometrica 48 (1980) 817) consistent estimator of the variance-covariance matrix in heteroskedastic models could be severely biased if the design matrix is highly unbalanced. In this paper we, therefore, reconsider Rao's (J. Amer. Statist. Assoc. 65 (1970) 161) minimum norm quadratic unbiased estimator (MINQUE). We derive the analytical expressions for the mean squared errors (MSE) of the Eicker-White, one of MacKinnon and White's (J. Econometrics 29 (1985) 305) and MINQUE estimators, and perform a numerical comparison. Our analysis shows that although MINQUE is unbiased by construction, it has very large variance particularly for the highly unbalanced design matrices. Since the variance is the dominant factor in our MSE computation, MINQUE is not the preferred estimator in terms of MSE comparison. We also studied the finite sample behavior of the confidence interval of regression coefficients in terms of coverage probabilities based on different variance-covariance matrix estimators. Our results indicate that although MINQUE generally has the largest MSE, it performs relatively well in terms of coverage probabilities.
AB - Chesher and Jewitt (Econometrica 55 (1987) 1217) demonstrated that the Eicker (Ann. Math. Statist. 34 (1963) 447) and White (Econometrica 48 (1980) 817) consistent estimator of the variance-covariance matrix in heteroskedastic models could be severely biased if the design matrix is highly unbalanced. In this paper we, therefore, reconsider Rao's (J. Amer. Statist. Assoc. 65 (1970) 161) minimum norm quadratic unbiased estimator (MINQUE). We derive the analytical expressions for the mean squared errors (MSE) of the Eicker-White, one of MacKinnon and White's (J. Econometrics 29 (1985) 305) and MINQUE estimators, and perform a numerical comparison. Our analysis shows that although MINQUE is unbiased by construction, it has very large variance particularly for the highly unbalanced design matrices. Since the variance is the dominant factor in our MSE computation, MINQUE is not the preferred estimator in terms of MSE comparison. We also studied the finite sample behavior of the confidence interval of regression coefficients in terms of coverage probabilities based on different variance-covariance matrix estimators. Our results indicate that although MINQUE generally has the largest MSE, it performs relatively well in terms of coverage probabilities.
KW - Linear regression model
KW - MINQUE
KW - Unbiasedness
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U2 - 10.1016/S0378-3758(02)00274-4
DO - 10.1016/S0378-3758(02)00274-4
M3 - Article
AN - SCOPUS:0036840399
SN - 0378-3758
VL - 108
SP - 121
EP - 136
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1-2
ER -