Authors

• Michele Crescenzi
• Malay Ghosh
• Tapabrata Maiti

Abstract

The paper proposes empirical Bayes (EB) estimators for
simultaneous estimation of means in the natural exponential family
(NEF) with quadratic variance functions (QVF) models. Morris
(1982, 1983a) characterized the NEF-QVF distributions which include
among others the binomial, Poisson and normal distributions.
In addition to the EB estimators, we provide approximations to the
MSE’s of these estimators. Our approach generalizes the findings of
Prasad and Rao (1990) for the random effects model where only area
specific direct estimators and covariates are available. The EB estimators
are derived using the theory of optimal estimating functions
as proposed by Godambe and Thompson (1989). This is in contrast
to the approach of Morris (1988) who found some approximate EB
estimators for this problem. Also, unlike Morris (1988), we allow unequal
number of observations in different clusters in the derivation of
the EB estimators. In finding approximations to the MSE’s, we apply
a bias-correction technique as proposed in Cox and Snell (1968). We illustrate our methodology by reanalyzing the toxoplasmosis data of
Efron (1978, 1986).

Keywords

• Estimating function
• Mean squared error
• toxoplasmosis data