Modern Stochastics: Theory and Applications

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.