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Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

Published online by Cambridge University Press:  11 February 2009

Anoop Chaturvedi ,
Hikaru Hasegawa ,
Ajit Chaturvedi  and
Govind Shukla
Anoop Chaturvedi
Affiliation:
University of Allahabad
Hikaru Hasegawa
Affiliation:
Hokkaido University
Ajit Chaturvedi
Affiliation:
Meerut University
Govind Shukla
Affiliation:
University of Allahabad
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Abstract

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 3 , June 1997 , pp. 406 - 429
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCE

Carter, R.A.L., M.S. Srivastava, V.K. Srivastava, & Ullah, A. (1990) Unbiased estimation of the MSE matrix of Stein-rule estimators, confidence ellipsoids, and hypothesis testing. Econometric Theory 6, 63–74.CrossRefGoogle Scholar
Chaturvedi, A. & Shukla, G. (1990) Stein rule estimation in the linear model with nonscalar error covariance matrix. Sanhya 52B, 293–304.Google Scholar
Dagpunar, J. (1988) Principles of Random Variate Generation. Oxford: Oxford University Press.Google Scholar
Judge, G.G. & Bock, M.E. (1978) The Statistical Implication of Pre-test and Stein-Rule Estimators in Econometrics. Amsterdam: North-Holland.Google Scholar
Judge, G.G., Griffiths, W.E., Hill, R.C., Liitkepohl, H., & Lee, T.C. (1985) The Theory and Practice of Econometrics, 2nd ed.New York: John Wiley.Google Scholar
Menjoge, S.S. (1984) On double k-class estimators of coefficients in linear regression. Economics Letters 15, 295–300.CrossRefGoogle Scholar
Nickerson, D.M. & Basawa, I.V. (1992) Shrinkage estimation for linear models with correlated errors. SanhyS 54A, 411–424.Google Scholar
Phillips, P.C.B. (1984) The exact distribution of the Stein rule estimator. Journal of Econometrics 25, 123–132.CrossRefGoogle Scholar
Rao, C.R. (1973) Linear Statistical Inference and Its Applications, 2nd ed.New York: John Wiley.CrossRefGoogle Scholar
Ripley, B.D. (1987) Stochastic Simulation. New York: John Wiley.CrossRefGoogle Scholar
Rothenberg, T.J. (1984) Approximate normality of generalized least squares estimators. Econometrica 52, 811–825.CrossRefGoogle Scholar
Srivastava, V.K. & Ullah, A. (1980) On Lindley like mean correction in the improved estimation of linear regression models. Economics Letters 6, 29–35.CrossRefGoogle Scholar
Ullah, A. (1982) The approximate distribution of the Stein rule estimators. Economics Letters 10, 305–308.CrossRefGoogle Scholar
Ullah, A., R.A.L. Carter, & Srivastava, V.K. (1984) The sampling distribution of shrinkage estimators and their F-ratios in the regression model. Journal of Econometrics 25, 109–122.CrossRefGoogle Scholar
Ullah, A. & Ullah, S. (1978) Double k-class estimators of coefficients in linear regression. Econometrica 46, 705–722.CrossRefGoogle Scholar
Vinod, H.D. & Ullah, A. (1981) Recent Advances in Regression Models. New York: Marcel Dekker.Google Scholar