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Abstract: This paper shows that large nonparametric classes of conditional multivariatedensities can be approximated in the Kullback-Leibler distance by differentspecifications of finite mixtures of normal regressions in which normal meansand variances and mixing probabilities can depend on variables in theconditioning set covariates. These models are a special case of models knownas -mixtures of experts- in statistics and computer science literature.Flexible specifications include models in which only mixing probabilities,modeled by multinomial logit, depend on the covariates and, in the univariatecase, models in which only means of the mixed normals depend flexibly on thecovariates. Modeling the variance of the mixed normals by flexible functions ofthe covariates can weaken restrictions on the class of the approximabledensities. Obtained results can be generalized to mixtures of general locationscale densities. Rates of convergence and easy to interpret bounds are alsoobtained for different model specifications. These approximation results can beuseful for proving consistency of Bayesian and maximum likelihood densityestimators based on these models. The results also have interestingimplications for applied researchers.



Autor: Andriy Norets

Fuente: https://arxiv.org/







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