Permutation-based uncertainty quantification about a mixing distribution

TL;DR

This paper introduces a permutation-based method for uncertainty quantification in nonparametric mixing distribution estimation, providing valid confidence intervals through a novel use of the predictive recursion algorithm.

Contribution

It develops a permutation-based approach to quantify uncertainty in mixing distribution estimates obtained via predictive recursion, addressing a gap in nonparametric mixture model inference.

Findings

The method produces approximately valid confidence intervals.

Theoretical results support the validity of the approach.

Numerical experiments demonstrate practical effectiveness.

Abstract

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing distribution. This paper focuses on estimation via the predictive recursion algorithm, and here we take advantage of this estimator's seemingly undesirable dependence on the data ordering to obtain a permutation-based approximation of the sampling distribution which can be used to quantify uncertainty. Theoretical and numerical results confirm that the proposed method leads to valid confidence intervals, at least approximately.