An efficient variant of dual to product and ratio estimators in sample surveys

Sayed Zeeshan,Gajendra K Vi̇shwakarma,Manish Kumar

doi:10.31801/cfsuasmas.808888

Abstract

This manuscript considers a dual to product and ratio estimator for estimating the finite population mean of study variable on applying a simple transformation to the auxiliary variable by using its average values in the population that is generally available in practice. The mean square error (MSE) of the proposed estimator has been obtained to the first degree of approximation. The optimum values and range of suitably chosen scalar, under which the proposed estimator perform better, have been determined. A method to lower the MSE of the proposed estimator relative to that of the MSE of the linear regression estimator is developed for small sample sizes. Theoretical and empirical studies have been done to demonstrate the superiority of the proposed estimator over the other estimators.

Highlights

This manuscript considers a dual to product and ratio estimator for estimating the finite population mean of study variable on applying a simple transformation to the auxiliary variable by using its average values in the population that is generally available in practice
A method to lower the mean square error (MSE) of the proposed estimator relative to that of the MSE of the linear regression estimator is developed for small sample sizes
There are numerous number of ratio and product type estimators available in survey literature from the time ratio estimator was developed by Cochran [4], and the product estimator was defined by Robson [12] that was revisited by Murthy [11]

Summary

Introduction

There are numerous number of ratio and product type estimators available in survey literature from the time ratio estimator was developed by Cochran [4], and the product estimator was defined by Robson [12] that was revisited by Murthy [11]. This has led to the accumulation of a large number of the ratio as well as product type estimators with cumbersome structure over the time. (19) to (21) and Eq (25) substantiate that the modified ratio and product type estimators are too complex in structure, demands advance knowledge of the scalars and the minimum MSEs of these estimators are equivalent to the MSE of linear regression estimator Y ̄reg as given in Eq (9). Where w denotes the scalar which is to be suitably determined so as to minimize the MSE of the above concerned estimator Squaring both sides of Eq (38), taking the expectation and using results in Eq (27), we obtain the MSE of Y ̄w to the first degree of approximation as.

Bias and Efficiency Comparisons

Empirical Study

Discussion and Conclusion