Linear regression by observations from mixture with varying concentrations

TL;DR

This paper introduces a modified least-squares estimator for linear regression in finite mixture models with varying mixing probabilities, demonstrating its consistency and asymptotic normality.

Contribution

It proposes a new estimator tailored for mixture models with varying probabilities and proves its statistical properties.

Findings

Estimator is consistent.

Estimator is asymptotically normal.

Applicable to mixture models with varying mixing probabilities.

Abstract

We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the least-squares estimator is proposed for estimation of the regression coefficients. Consistency and asymptotic normality of the estimates is demonstrated.