Consistency of local linear regression estimator for mixtures with varying concentrations

Abstract

Finite mixtures with different regression models for different mixture components naturally arise in statistical analysis of biological and sociological data. In this paper a model of mixtures with varying concentrations is considered in which the mixing probabilities are different for different observations. A modified local linear estimation (mLLE) technique is developed to estimate the regression functions of the mixture component nonparametrically. Consistency of the mLLE is demonstrated. Performance of mLLE and a modified Nadaraya–Watson estimator (mNWE) is assessed via simulations. The results confirm that the mLLE technique overcomes the boundary effect typical to the NWE.

Keywords

• Nonparametric regression
• mixture with varying concentrations
• boundary effect
• consistency