Statistical Inference for Scale Mixture Models via Mellin Transform Approach

TL;DR

This paper introduces a Mellin transform-based method for statistical inference in scale mixture models, providing theoretical error analysis and numerical validation for both discrete and continuous mixing distributions.

Contribution

It develops a novel Mellin transform approach for inference in scale mixture models and proves a Berry-Esseen type inequality for Mellin transforms.

Findings

The method achieves accurate estimation in scale mixture models.

Theoretical error bounds are established for the Mellin-based estimates.

Numerical examples demonstrate the approach's effectiveness.

Abstract

This paper deals with statistical inference for the scale mixture models. We study an estimation approach based on the Mellin -- Stieltjes transform that can be applied to both discrete and absolute continuous mixing distributions. The accuracy of the corresponding estimate is analysed in terms of its expected pointwise error. As an important technical result, we prove the analogue of the Berry -- Esseen inequality for the Mellin transforms. The proposed statistical approach is illustrated by numerical examples.