An Improved Class of Chain Ratio-Product Type Estimators in Two-Phase Sampling Using Two Auxiliary Variables

Gajendra K Vishwakarma,Manish Kumar

doi:10.1155/2014/939701

Gajendra K Vishwakarma, Manish Kumar

Open Access

https://doi.org/10.1155/2014/939701

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Abstract

This paper presents a technique for estimating finite population mean of the study variable in the presence of two auxiliary variables using two-phase sampling scheme when the regression line does not pass through the neighborhood of the origin. The properties of the proposed class of estimators are studied under large sample approximation. In addition, bias and efficiency comparisons are carried out to study the performances of the proposed class of estimators over the existing estimators. It has also been shown that the proposed technique has greater applicability in survey research. An empirical study is carried out to demonstrate the performance of the proposed estimators.

Highlights

This paper presents a technique for estimating finite population mean of the study variable in the presence of two auxiliary variables using two-phase sampling scheme when the regression line does not pass through the neighborhood of the origin
The use of auxiliary information for estimating population mean of the study variable has greater applicability in survey research
The ratio estimator was developed by Cochran [1] to estimate the population mean Y of the study variable Y by using information on auxiliary variable X, positively correlated with Y

Summary

Introduction

The use of auxiliary information for estimating population mean of the study variable has greater applicability in survey research. When the population mean X of the auxiliary variable X is not known before the start of a survey, a firstphase sample of size n󸀠 is selected from the population of size N on which only the auxiliary variable X is measured in order to furnish a good estimate of X. We can use either one or two (or more than two) auxiliary variables while estimating population mean of the study variable; keeping this fact, Chand [11] introduced chain ratio estimators This led various authors including Kiregyera [12], Singh and Upadhyaya [13], Prasad et al [14], Singh et al [15], Singh and Choudhury [16], and Vishwakarma and Gangele [17] to modify the chain type estimators and discuss their properties. Y and x are the sample means of Y and X, respectively, based on the second-phase sample of size n drawn from the first-phase sample of size n󸀠 with the help of SRSWOR scheme

Proposed Estimator

Bias and MSE of the Proposed Estimator

Empirical Study

Conclusion