Large Sample Inference in Finite Population Problems

Abstract

In sample survey, estimation of different finite population parameters like, mean, median, variance, coefficient of variation, correlation and regression coefficients, interquartile range, measure of skewness, etc. was considered extensively in the past. However, comparison of different estimators of the same parameters has been limited. Also, asymptotic theory for several estimators has not been adequately developed. One of the main objectives of this Ph.D. thesis is to compare various well-known estimators of finite population parameters under different sampling designs based on their asymptotic distributions. Another objective of this thesis is to understand the role of auxiliary information in the implementation of different sampling designs and in the construction of different estimators. Four different chapters in this thesis focus on four major topics. In the second chapter, several well-known estimators of the finite population mean and its functions are compared under some commonly used sampling designs. A similar comparison is carried out in the third chapter for the case of mean, when the data are infinite dimensional in nature. In the fourth chapter, the weak convergence of different quantile processes are shown under several sampling designs and superpopulation distributions, and these results are used to study asymptotic properties of estimators of various finite population parameters. Finally, in the fifth chapter, the asymptotic behaviour of the estimators obtained from different regression methods are studied in the context of sample survey.