Use of Auxiliary Variables and Asymptotically Optimum Estimators in Double Sampling

M. E. Kanwai,A. Isah,O. E. Asiribo

doi:10.5539/ijsp.v5n3p55

M. E. Kanwai, A. Isah + Show 1 more

Open Access

https://doi.org/10.5539/ijsp.v5n3p55

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Abstract

This paper explore the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators. The study proposed two types of estimators with two auxiliary variables for two phase sampling when there is no information about auxiliary variables at population level. The expressions for the Mean Squared Error (MSE) of the proposed estimators were derived to the first order of approximation. An empirical comparative approach of the minimum variances and percent relative efficiency were adopted to study the efficiency of the proposed and existing estimators. It was established that, the proposed estimators performed more efficiently than the mean per unit estimator and other previous estimators that don’t use auxiliary variable and that are not asymptotically optimum. Also, it was established that estimators that are asymptotically optimum that utilized single auxiliary variable are more efficient than those that are not asymptotically optimum with two auxiliary variables.

Highlights

IntroductionThere are times when information is available on every unit in the population
In survey research, there are times when information is available on every unit in the population
This paper explores the need for exploiting auxiliary variables in sample survey and utilizing asymptotically optimum estimator in double sampling to increase the efficiency of estimators

Summary

Introduction

There are times when information is available on every unit in the population. General intuitive variable of interest, can be improved if the information supplied by a related variable (auxiliary variable, supplementary variable, or concomitant variable).When two or more auxiliary variables are available; many estimators may be defined by linking together different estimators such as ratio, product or regression, each one of them exploiting a single variable. These mixed estimators have been seen performing better as compared with individual estimators.

Research Design

Analytical Techniques

Sampling without Auxiliary Variable

Notations and the Proposed Estimators

Empirical Study

Discussions of Results

Conclusions