Unbiased Ratio-Type Estimator Using Transformed Auxiliary Variable In Negative Correlation Case

TL;DR

This paper introduces a new unbiased ratio-type estimator for finite population means with negatively correlated variables, improving estimation accuracy by leveraging transformed auxiliary variables.

Contribution

It proposes a novel unbiased estimator that generalizes existing methods and derives its variance expression, enhancing estimation in negative correlation scenarios.

Findings

The proposed estimator outperforms Robson's estimator in empirical tests.

It generalizes Hartley-Ross and Singh-Singh estimators.

Variance expression derived for practical application.

Abstract

The objective of this paper is to propose an unbiased ratio-type estimator for finite population mean when the variables are negatively correlated. Hartley and Ross[2] and Singh and Singh [6] estimators are identified as particular cases of the proposed unbiased estimator. The variance expression of the proposed estimator to the first degree of approximation has been obtained. An empirical study is carried out to demonstrate the performance of the proposed estimator over, Robson [5] estimator and Singh and Singh [6] estimator.