EM algorithms for estimating the Bernstein copula

Xiaoling Dou; Satoshi Kuriki; Gwo Dong Lin; Donald Richards

doi:10.1016/j.csda.2014.01.009

EM algorithms for estimating the Bernstein copula

Xiaoling Dou, Satoshi Kuriki, Gwo Dong Lin, Donald Richards

Research output: Contribution to journal › Article

8 Citations (Scopus)

Abstract

A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent various distributions flexibly and that the proposed EM algorithms work well for such data.

Original language	English
Pages (from-to)	228-245
Number of pages	18
Journal	Computational Statistics and Data Analysis
Volume	93
DOIs	https://doi.org/10.1016/j.csda.2014.01.009
Publication status	Published - 2016 Jan 1
Externally published	Yes

Keywords

Baker's distribution
Bernstein polynomial
Density estimation
Linear convergence
Order statistic
Ordered categorical data

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Statistics and Probability
Applied Mathematics

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Dou, X., Kuriki, S., Lin, G. D., & Richards, D. (2016). EM algorithms for estimating the Bernstein copula. Computational Statistics and Data Analysis, 93, 228-245. https://doi.org/10.1016/j.csda.2014.01.009

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AU - Richards, Donald

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AB - A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization (EM) algorithms to estimate the Bernstein copula are proposed, and a local convergence property is proved. Moreover, asymptotic properties of the proposed semiparametric estimators are provided. Illustrative examples are presented using three real data sets and a 3-dimensional simulated data set. These studies show that the Bernstein copula is able to represent various distributions flexibly and that the proposed EM algorithms work well for such data.

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KW - Density estimation

KW - Linear convergence

KW - Order statistic

KW - Ordered categorical data

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