Estimation of variance components with applications in sample surveys

Abstract

This thesis is concerned with the problem of variance components estimation and its applications in sample survey.

The MINQUE (minimum norm invariant quadratic unbiased estimator) was proposed for a general variance components model, but its optimality requires normality assumption and correct prior values. A sufficient condition for optimality is given in the thesis as an alternative condition to the normality assumption. A necessary and sufficient condition is proved for MINQUE to be independent of prior values and a simplified condition is given for the balanced analysis of variance models.

There are several modified versions of MINQUE that yield nonncgative estimates for the variance components. In this thesis the noncxistcnce of a nonnegative minimum biased quadratic estimator across the parameter space is proved. A nonnegative estimator, which has minimum variance among all the estimators minimizing an upper bound of the bias function, is proposed. Numerical and empirical studies arc carried out and suggestions are made on the use of these nonnegative estimators.

MINQUE is applied to estimate the interviewer's variance in a complex sample survey and its efficiency is compared with some existing estimators.

An optimal design with a specified cost constraint is given and an unbiased

estimator for the variance of the estimator of the mean is derived.

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