Estimating ordered variance of two scale mixture of normal distributions

TL;DR

This paper develops improved estimators for ordered variances in scale mixture of two normal distributions, including multivariate t-distributions, using squared error and entropy loss functions, supported by theoretical and numerical validation.

Contribution

It introduces new estimators that outperform existing methods for estimating ordered variances in scale mixtures of normals, with specific focus on multivariate t-distributions.

Findings

Derived general improvement results for estimators

Proposed classes of improved estimators under certain conditions

Validated theoretical results with numerical comparisons

Abstract

This study investigates component wise estimation of ordered variances of scale mixture of two normal distributions. For this study two special loss functions are considered namely squared error loss function and entropy loss function. We have derived the general improvement results and based on these results the estimators that outperform BAEE are obtained. Moreover under certain sufficient conditions a class of improved estimators is proposed for both loss functions. As a special case of scale mixture of normal distribution the results are applied to the multivariate t-distribution and obtained the improvement results. For this case a detailed numerical comparison is carried out which validates our theoretical findings.