Asymptotic normality of local linear regression estimator for mixtures with varying concentrations
Pub. online: 2 September 2025
Type: Research Article
Open Access
Open Access
Received
27 June 2025
27 June 2025
Revised
6 August 2025
6 August 2025
Accepted
7 August 2025
7 August 2025
Published
2 September 2025
2 September 2025
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. The modified local linear regression estimator (mLLRE) is considered for nonparametric estimation of the unknown regression function for the given component of mixture. The asymptotic normality of the mLLRE is proved in the case when the regressor’s probability density function has jumps. Theoretically optimal bandwidth is derived. Simulations were made to estimate the accuracy of the normal approximation.
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