A Class of Estimators of Population Variance Using Auxiliary Information in Sample Surveys

Abstract

This article advocates the problem of estimating the population variance of the study variable using information on certain known parameters of an auxiliary variable. A class of estimators for population variance using information on an auxiliary variable has been defined. In addition to many estimators, usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999), and Kadilar and Cingi's (2006) estimators are shown as members of the proposed class of estimators. Asymptotic expressions for bias and mean square error of the proposed class of estimators have been obtained. An empirical study has been carried out to judge the performance of the various estimators of population variance generated from the proposed class of estimators over usual unbiased estimator, Isaki's (1983), Upadhyaya and Singh's (1999) and Kadilar and Cingi's (2006) estimators.

Keywords:

• Auxiliary variable
• Bias
• Mean square error
• Study variable

Acknowledgment

The authors are thankful to Indian School of Mines, Dhanbad and Vikram University, Ujjain for providing the facilities to carry out the research work. The authors are very grateful to the learned referees for their valuable suggestions.