A Generalized Family of Transformed Ratio-Product Estimators for Variance in Sample Surveys

Abstract

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

Keywords:

• Auxiliary variate
• Bias
• Mean squares error
• Product estimator
• Ratio estimator
• Study variate
• Transformed variable

Acknowledgments

The authors acknowledge the University Grants Commission, New Delhi, India for financial support in the project number F. No. 34-137/2008(SR). The authors are also thankful to Indian School of Mines, Dhanbad and Vikram University, Ujjain for providing the facilities to carry out the research work. The authors are also grateful to the referees for a valuable suggestions regarding improvement of the article.