Bernstein Polynomial Model for Nonparametric Multivariate Density
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2019
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Taylor and Francis
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Abstract
In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood estimate can be obtained using EM algorithm. A change-point method of choosing optimal degrees of the proposed Bernstein polynomial model is presented. Under some conditions, the optimal rate of convergence in the mean -divergence of new density estimator is shown to be nearly parametric. The method is illustrated by an application to a real data set. Finite sample performance of the proposed method is also investigated by simulation study and is shown to be much better than the kernel density estimate but close to the parametric ones.
Keywords: Approximate Bernstein polynomial model; beta mixture; maximum likelihood; multivariate density estimation; nonparametric model
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Tao Wang, Zhong Guan. (2019) Bernstein polynomial model for nonparametric multivariate density. Statistics 53:2, pages 321-338.
This is an Accepted Manuscript of an article published by Taylor & Francis in Statistics on Feb.06,2019, available online: https://doi.org/10.1080/02331888.2019.1574299 .
This is an Accepted Manuscript of an article published by Taylor & Francis in Statistics on Feb.06,2019, available online: https://doi.org/10.1080/02331888.2019.1574299 .
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