Confidence ellipsoids for regression coefficients by observations from a mixture

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.

Keywords

• Finite mixture model
• Linear regression
• mixture with varying concentrations
• nonparametric estimation
• maximum likelihood
• confidence ellipsoid