Enhancing efficiency of ratio-type estimators of population variance by a combination of information on robust location measures

Document Type: Article

Authors

1 Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou 310027, People’s Republic of China

2 Faculty of Physical Sciences, Department of Statistics, Government College University Faisalabad, Pakistan

3 1: Faculty of Physical Sciences, Department of Statistics, Government College University Faisalabad, Pakistan. 2: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China.

4 Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou 310027, People’s Republic of China.

Abstract

Numerous ratio-type estimators of the population variance are proposed in the existing literature based on different characteristics of the study as well as the auxiliary variable. However, mostly the existing estimators are based on the conventional measures of the population characteristics and their efficiency is dubious in the presence of outliers in the data. This study presents improved families of variance estimators under simple random sampling without replacement assuming that the information on some robust non-conventional location parameters of the auxiliary variable is known besides the usual conventional parameters. The bias and mean square error of the proposed families of estimators are obtained and the efficiency conditions are derived mathematically. The theoretical results are supplemented with the numerical illustrations by using real datasets which indicates the supremacy of the suggested families of estimators.

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