Multivariate dual to ratio type estimators using arithmetic, geometric and harmonic means in simple random sampling

TL;DR

This paper introduces new multivariate ratio estimators based on arithmetic, geometric, and harmonic means in simple random sampling, aiming to improve estimation efficiency using auxiliary information.

Contribution

It proposes novel estimators utilizing multiple auxiliary variables with different mean-based approaches, analyzing their bias and mean squared error properties.

Findings

Harmonic and geometric mean estimators are more biased than arithmetic mean estimators under certain conditions.

All three estimators have the same first-order mean squared error.

The proposed estimators effectively utilize auxiliary information to enhance estimation accuracy.

Abstract

Auxiliary variable is extensively used in survey sampling to improve the precision of estimates. Whenever there is availability of auxiliary information, we want to utilize it in the method of estimation to obtain the most efficient estimator. In this paper using multi-auxiliary information we have proposed estimators based on arithmetic, geometric and harmonic mean. It was also shown that estimator based on harmonic and geometric means are more biased than estimator based on arithmetic mean under certain conditions. However, the MSE of all three estimators are same up to the first order of approximation.