Abstract:
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Finite mixture regression (FMR) models are powerful modeling tools to analyze data of various types because of FMR's flexible model structure and appealing interpretation. Applications can be found in a variety of areas, such as economics, finance and clinical trials. In this paper, we focus on the logistic-normal mixture models, which allow both the mixing parameters and the mean parameters to vary with covariates. In addition, we consider the scenario where the number of the potential covariates grows with the sample size. In this situation, the likelihood function becomes non-convex, and the traditional techniques for analyzing model selection with high dimensional data do not work. We show under appropriate conditions that the LASSO type estimators of the FMR models remain consistent in terms of Kullback-Leibler divergence, and moreover, an upper bound for the zero-coefficient estimates can be established.
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