Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 3 , pp. 334 -- 355

PRE-TEST ESTIMATION OF THE REGRESSION SCALE PARAMETER WITH MULTIVARIATE STUDENT-t ERRORS AND INDEPENDENT SUB-SAMPLES

By

JUSTON ANDERSON, NZ Ministry of Housing

and

JUDITH A. GILES, University of Victoria

SUMMARY. We consider the estimation of the error variance of a regression when additional information is available in the form of a second sample, which may be generated from a process with the same variance. This problem has received attention in the literature when the joint errors are members of the spherically symmetric family. We extend this assumption to one in which the errors in each sample are independent multivariate Student-t random vectors. We derive the exact risk under quadratic loss of the pre-test estimator which results after a test for homogeneity of the variances and we compare the risk of this estimator with that of its component estimators.

AMS (1980) subject classification. Primary 62J05, 62F11; secondary 62P20.

Key words and phrases. Preliminary testing , conditional inference, non-normal disturbances, testing for homogeneity.

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