A multiplicative bias reduction for nonparametric approach and the two sample problem in a sample survey

Abstract

This study carries on the problem of nonparametric estimation of nite population total using multiplicative bias correction technique for two sample problem in a sample survey is considered. Let two separate surveys collect related information on a single population U. Consider a situation where we want to best combine data from the two surveys to yield a single set of estimates of a population quantity (\population parameter") of interest. This thesis presents a multiplicative bias reduction estimator for nonparametric regression to two sample problem in a sample survey. The approach consists of applying a multiplicative bias correction to an estimator. The multiplicative bias correction method which was proposed, by Linton & Nielsen, 1994, assures a positive estimate and reduces the bias of the estimate with negligible increase in variance. Even as we apply this method to the two sample problem in a sample survey, we found out through the study of it asymptotic properties that it was asymptotically unbiased and statistically consistent. Furthermore, an empirical study was carried out to compare the performance of the developed estimator with the existing ones. The theoretical and empirical results led to the conclusion that the multiplicative bias corrected estimator can be highly recommended for two sample problem in sample survey when estimating the nite population total.