A New Family of Estimators of the Population Variance using Information on Population Variance of Auxiliary Variable in Sample Surveys

Abstract

This paper proposes a family of estimators of population variance 2 y S of the study variable y in the presence of known population variance 2 x S of the auxiliary variable x. It is identified that in addition to many, the recently proposed classes of estimators due to Sharma and Singh (2014) and Singh and Pal (2016) are members of the proposed family of estimators. Asymptotic expressions of bias and mean squared error (MSE) of the suggested family of estimators have been obtained. Asymptotic optimum estimator (AOE) in the family of estimators is identified. Some subclasses of estimators of the proposed family of estimators have been identified along with their properties. We have also given the theoretical comparisons among the estimators discussed in this paper. ASM Classification: 62D05.

Improved estimation of population variance using information on auxiliary attribute in simple random sampling

“…In It has been also observed that the suggested class of estimators M t under optimum condition is more efficient than usual unbiased estimator, usual regression estimator, Singh and Kumar (2011) estimator and other estimators discussed in this paper.…”

“…In order to have an estimate of the study variable y, assuming the knowledge of the population proportion P, Singh and Kumar (2011) proposed the following estimators…”

Estimation of Finite Population Variances using Auxiliary Attribute in Sample Surveys

“…The expressions of bias and MSEs have been derived up to the first order of approximation. It has been shown that the performance of the proposed estimators is better than the usual unbiased estimator, usual ratio estimators and estimators due to Singh and Kumar (2011). In addition, an empirical study is carried out in the support of theoretical results.…”

“…In this section we have suggested some estimators of population variance based on usual unbiased estimator, usual ratio estimators and estimators due to Singh and Kumar (2011). The properties of the suggested estimators have been obtained up to the first degree of approximation.…”

“…It is assumed that attribute  takes only the two values 0 and 1 according as  =1, if ith unit of the population possesses attribute  =0, if otherwise. The usual unbiased estimator for population variance of the study variable Y is defined by   Using information on the population variance 2 S  of the auxiliary attribute  , Singh and Kumar (2011) proposed the following estimators Singh et al (2011), we proposed some estimators of population variance of study variable Y using auxiliary attribute based on arithmetic mean, geometric mean and harmonic mean of the estimators  …”