Higher order calibrated estimator in two-stage sampling

Abstract

In this paper, we consider a situation when the population variances of the auxiliary variable in the first stage units selected in a sample are known in addition to the known population means of the auxiliary variable. The higher order calibration weights which make use of both the population variances and population means at the estimation stage for both the first stage units and the second stage units selected in the sample are derived. The resultant estimator is found to be consistent estimator, and has variance smaller than the existing estimators in the literature. The percent relative efficiency of the proposed estimator over the linear regression estimator has been demonstrated through numerical comparisons.

Keywords:

• Auxiliary information
• two-stage sampling
• estimation of mean
• relative efficiency

Acknowledgments

The authors are thankful to the Editor-in-Chief Prof. Narayanaswamy Balakrishnan, Admins. Flincy Kulandhaisamy, Mrs. Debbie Iscoe and a referee for their valuable comments on the original version of this manuscript. Thanks are also due to Ms. Shameem Alam, a visiting Ph.D. scholar at the Department of Mathematics, Texas A&M University-Kingsville for rechecking the derivations of the results.