Statistical Inference with Data Augmentation and Parameter Expansion

TL;DR

This paper explores data augmentation and parameter expansion techniques to improve statistical inference, demonstrating how these methods can reduce error bounds and enhance test efficiency.

Contribution

It introduces a novel measure R for assessing the impact of activating additional components in sufficient statistics, advancing the understanding of parameter expansion effects.

Findings

Parameter expansion reduces the upper bound on error probabilities.

Data augmentation provides more representative population information.

The measure R quantifies the effect of activating additional components.

Abstract

Statistical pragmatism embraces all efficient methods in statistical inference. Augmentation of the collected data is used herein to obtain representative population information from a large class of non-representative population's units. Parameter expansion of a probability model is shown to reduce the upper bound on the sum of error probabilities for a test of simple hypotheses, and a measure, R, is proposed for the effect of activating additional component(s) in the sufficient statistic.