Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations

TL;DR

This paper introduces an algorithm for consistently estimating identifiable nonparametric mixture models from grouped data, even with overlapping components, advancing the theoretical understanding and practical estimation methods.

Contribution

It proposes a novel algorithm that guarantees consistent estimation of mixture models from grouped observations, extending identifiability results to nonparametric and overlapping components.

Findings

Algorithm outperforms existing methods with overlapping components

Leverages oracle inequality for kernel density estimators

Ensures consistent estimation from grouped data

Abstract

Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap. This work proposes an algorithm that consistently estimates any identifiable mixture model from grouped observations. Our analysis leverages an oracle inequality for weighted kernel density estimators of the distribution on groups, together with a general result showing that consistent estimation of the distribution on groups implies consistent estimation of mixture components. A practical implementation is provided for paired observations, and the approach is shown to outperform existing methods, especially when mixture components overlap significantly.