Advancing Sampling Techniques: Multivariate Ratio Estimation for Variance Vector in Two-Phase Sampling

Abstract

The problem of variance vector estimation using multi-auxiliary variables is not quite often considered in the literature. In the present study, we propose a multivariate ratio estimation approach for estimating a vector of variances in two-phase sampling using a vector of  variables, following the situation if the desired parameters are available only for some of the auxiliary variables.  Some special cases of the proposed generalized multivariate variance estimator have also been discussed. Expressions of the bias, and generalized variance has been derived. With the help of real-life data, the applicability of the proposed multivariate variance estimator has been given, and it is shown that the proposed multivariate estimator is more efficient than the modified versions of multivariate variance estimators. A simulation study has also been carried out to show that the proposed estimator surpasses the modified version of multivariate estimators.