# Admissible Estimation of a Finite Population Total under PPS Sampling

Author Affiliations

^{1}Department of Statistics, Sardar Patel University, Vallabh Vidyanagar 388 120, India^{2}St. Xevier’s College, Gujarat University, Ahmedabad-380 009, India

*Res. J. Mathematical & Statistical Sci.,* **Volume 4, Issue (10),** Pages 10-15, November,12 **(2016)**

## Abstract

The probability proportion to size (PPS) and with replacement estimator is inadmissible since it depends on multiplicity. An improve estimator is available but it is too complicated. Using the Bayes prediction approach a Bayes predictor, based on the distinct units of the sample selected with PPS sampling, is constructed which includes a generalized difference estimator of the population total. Moreover, using the limiting Bayes risk method it is shown that this predictor is admissible. For comparison of the suggested estimator, a generalize regression estimator and an optimal estimator (with distinct units) are discussed. Using real populations, a small scale Monte Carlo simulation is carried out for the comparison of estimators. It is found that the suggested estimator has performed very well for most of the real populations under investigation.

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