Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 1, pp. 95--108

AN OPTIMAL ESTIMATING EQUATION WITH UNSPECIFIED VARIANCES

By

ANUP DEWANJI, Indian Statistical Institute, Kolkata

and

LUE PING ZHAO, Fred Hutchinson Cancer Research Center, Seattle, WA

SUMMARY. In estimating equation technique for estimating the mean regression parameters, one important issue is how to choose the weights to improve the efficiency of the estimation. The key idea of this paper is to replace the weights with the empirically estimated covariances. We discuss regression of an outcome on a vector of covariates, and propose an optimal estimating equation approach which achieves asymptotic efficiency. Asymptotic normality of the regression parameter estimates is also established. A small simulation study indicates improved efficiency of this approach.

AMS (1991) subject classification.

Key words and phrases. Estimating equations, Generalized linear model, Mean regression, Kernel smoothing

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