Confidence ellipsoids for regression coefficients by observations from a mixture

TL;DR

This paper develops methods for constructing confidence ellipsoids for linear regression coefficients using data from mixtures with varying concentrations, employing nonparametric and maximum likelihood approaches.

Contribution

It introduces two novel approaches—weighted least squares and EM-algorithm based maximum likelihood—for confidence ellipsoid construction in mixture regression models.

Findings

Effective confidence ellipsoids are constructed for mixture regression coefficients.

The methods accommodate varying mixture concentrations.

The approaches are applicable in complex mixture regression scenarios.

Abstract

Confidence ellipsoids for linear regression coefficients are constructed by observations from a mixture with varying concentrations. Two approaches are discussed. The first one is the nonparametric approach based on the weighted least squares technique. The second one is an approximate maximum likelihood estimation with application of the EM-algorithm for the estimates calculation.