Consistency of local linear regression estimator for mixtures with varying concentrations
Volume 11, Issue 3 (2024), pp. 359–372
Pub. online: 19 March 2024
Type: Research Article
Open Access
Open Access
Received
22 January 2024
22 January 2024
Revised
26 February 2024
26 February 2024
Accepted
28 February 2024
28 February 2024
Published
19 March 2024
19 March 2024
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.
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