VARIANCE ESTIMATION IN SAMPLING THEORY USING MULTI-AUXILIARY VARIABLES

Abstract

This dissertation is one of the steps towards the area of estimation of population variance using multi-auxiliary variables under multi-phase sampling scheme. This work mainly considers full, incomplete and no information cases about the auxiliary variables. The importance of estimation of finite population variance under multi-phase sampling along with some previously proposed estimators are discussed in Chapter 1. In Chapters 2 and 3, some ratio-type and regression-type variance estimators for estimation of population variance using multi-auxiliary variables for single interest variable are proposed. To the solution of multi-purpose surveys, few generalized multi-variate ratio-type and regression-type variance estimators are discussed in Chapters 4 and 5 respectively. Chapters 6 and 7 highlight the solution to the problem when multi-attributes is to be dealt for the estimation of population variance under multi-phase sampling. The measurement error in variable of interest is taken into account in Chapters 8 and 9 for the same estimators proposed in Chapters 2 and 3. The expressions for minimum mean square error for all proposed estimators are also derived. Some real data sets are used for efficiency comparison.