Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 2 , pp. 173--192

SOMETIMES POOL ESTIMATOR OF REGRESSION COEFFICIENT WHEN CONDITIONAL VARIANCES ARE UNKNOWN AND UNEQUAL

By

A. K. SINGH and M. A. ALI, Indira Gandhi Agricultural University

and

H. R. SINGH, Ravi Shankar University

SUMMARY. The present paper proposes a sometimes-pool estimator of a regression coefficient in a two sample problem when the conditional variances are unknown and unequal. The expressions for bias, mean squared error of the proposed estimator along with its efficiency relative to the usual never pool estimator have been briefly derived. Some special results relating to bias and mean squared error (MSE) of the proposed estimator have been theoretically obtained for some specific values of nuisance parameter and preliminary levels of significance. The behaviours of bias, MSE and relative efficiency have been studied empirically. In the last, a criterion for recommendation of the level of significance for the preliminary test involved is given which ensures a desired level of efficiency.

AMS (1991) subject classification..

Key words and phrases. Preliminary test of significance, sometimes pool estimator, never pool estimator.

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