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Estimation of the Covariance Matrix of the Least-Squares Regression Coefficients When the Disturbance Covariance Matrix Is of Unknown Form

Published online by Cambridge University Press:  11 February 2009

Robert W. Keener ,
Jan Kmenta  and
Neville C. Weber
Robert W. Keener
Affiliation:
University of Michigan, Ann Arbor
Jan Kmenta
Affiliation:
University of Michigan, Ann Arbor
Neville C. Weber
Affiliation:
University of Sydney
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Abstract

This paper deals with the problem of estimating the covariance matrix of the least-squares regression coefficients under heteroskedasticity and/or autocorrelation of unknown form. We consider an estimator proposed by White [17] and give a relatively simple proof of its consistency. Our proof is based on more easily verifiable conditions than those of White. An alternative estimator with improved small sample properties is also presented.

Type
Articles
Information
Econometric Theory , Volume 7 , Issue 1 , March 1991 , pp. 22 - 45
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

1.Andrews, D.W.K. Heteroskedasticity and autocorrelation consistent cpvariance matrix estimation. Cowles Foundation Discussion Paper #877, Yale University, New Haven, July 1988.Google Scholar
2.Billingsley, P.Convergence of Probability Measures. New York: Wiley, 1968.Google Scholar
3.Calzolari, G. & Panattoni, L.. A simulation study on FIML covariance matrix. Centro Scientifico IBM, Pisa. Presented at the European Meeting of the Econometric Society, Madrid, 1984.Google Scholar
4.Cragg, J.G.More efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica 51 (1983): 751–763.CrossRefGoogle Scholar
5.Eicker, F.Asymptotic normality and consistency of the least squares estimators for families of linear regressions. Annals of Mathematical Statistics 34 (1963): 447–456.CrossRefGoogle Scholar
6.Eicker, F. Limit theorems for regressions with unequal and dependent errors. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Voh 1. Berkeley: University of California Press, 1967.Google Scholar
7.Hannan, E.J.Multiple Time Series. New York: Wiley, 1970.Google Scholar
8.Hinkley, D.V.Jackknifing in unbalanced situations. Technometrics 19 (1977): 285–292.CrossRefGoogle Scholar
9.Ibragimov, I.A. & Linnik, Y.V.. Independent and Stationary Sequences of Random Variables. The Netherlands: Wolters-Noordhoff 1971.Google Scholar
10Kool, H. A note on consistent estimation of heteroskedasticity and autocorrelated covariance matrices. Department of Econometrics, Free University, Amsterdam, 1988.Google Scholar
11MacKinnon, J.G. & White, H.. Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties. Journal of Econometrics 29 (1985): 305–325.Google Scholar
12Mokkadem, A.Sufficient conditions of geometric mixing for polynomial autoregressive processes-applications to ARM A processes and to bilinear processes. Compte Rendu 305, Series I (1987): 477–480.Google Scholar
13Newey, W.K. & West, K.D.. A simple positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55 (1987): 703–708.Google Scholar
14Robinson, P.M. Automatic generalized least squares. Department of Economics, London School of Economics, London, 1988.Google Scholar
15Sathe, S.T. & Vinod, H.D.. Bounds on the variance of regression coefficients due to heteroscedastic or autoregressive errors. Econometrica 42 (1974): 333–340.Google Scholar
16White, H.A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48 (1980): 817–838.Google Scholar
17White, H.Asymptotic Theory for Econometricians. Orlando: Academic Press, 1984.Google Scholar
18White, H. & Domowitz, I.. Nonlinear regression with dependent observations. Econometrica 52 (1984): 143–161.Google Scholar
19Withers, C.S.Conditions for linear processes to be strong-mixing. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 57 (1981): 477–480.Google Scholar