Estimating Parameters from Mixed Samples

Abstract

Assume that a sample is a mixture of two samples from two different populations with distributions F_θ1 and F_θ2 . Given the form of F_θ , estimators of θ₁ and θ₂ are introduced. It is shown that the estimators are consistent and their asymptotic joint distribution is derived. The suggested estimators are compared with the maximum likelihood estimators and the method of moments estimators. For small sample sizes the comparison is done by a Monte Carlo study. For large sample sizes the estimators are assessed by numerically computing their asymptotic variances.

Key Words:

• Parametric estimation
• Outliers
• Majorization and Schur convexity
• Maximum likelihood estimation
• Method of moments estimators
• Linear combinations of order statistics