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

Statistics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

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 (US)
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
State	Published - Jan 1 2016

All Science Journal Classification (ASJC) codes

Statistics and Probability
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1016/j.csda.2014.01.009

Cite this

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title = "EM algorithms for estimating the Bernstein copula",

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.",

author = "Xiaoling Dou and Satoshi Kuriki and Lin, \{Gwo Dong\} and Donald Richards",

note = "Funding Information: The authors thank the editor, the associate editor, and two referees for valuable and constructive comments and suggestions. The authors also thank the Illinois State Board of Education for permission to use the Illinois Standards Achievement Test scores data analyzed in Section 3.2 . The authors are also grateful to Shingo Shirahata, Toshihiko Shiroishi and Toyoyuki Takada for their helpful comments. This work was supported by the Systems Genetics Project of the Transdisciplinary Research Integration Center, Research Organization of Information and Systems . The manuscript was partially presented in the session on copulas of the 5th International Conference of the ERCIM WG on Computing \& Statistics (ERCIM 2012, 1–3 December 2012, Oviedo, Spain), and the initial manuscript was greatly improved by comments provided by the participants. Publisher Copyright: {\textcopyright} 2014 Elsevier B.V. All rights reserved.",

year = "2016",

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doi = "10.1016/j.csda.2014.01.009",

language = "English (US)",

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pages = "228--245",

journal = "Computational Statistics and Data Analysis",

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T1 - EM algorithms for estimating the Bernstein copula

AU - Dou, Xiaoling

AU - Kuriki, Satoshi

AU - Lin, Gwo Dong

AU - Richards, Donald

N1 - Funding Information: The authors thank the editor, the associate editor, and two referees for valuable and constructive comments and suggestions. The authors also thank the Illinois State Board of Education for permission to use the Illinois Standards Achievement Test scores data analyzed in Section 3.2 . The authors are also grateful to Shingo Shirahata, Toshihiko Shiroishi and Toyoyuki Takada for their helpful comments. This work was supported by the Systems Genetics Project of the Transdisciplinary Research Integration Center, Research Organization of Information and Systems . The manuscript was partially presented in the session on copulas of the 5th International Conference of the ERCIM WG on Computing & Statistics (ERCIM 2012, 1–3 December 2012, Oviedo, Spain), and the initial manuscript was greatly improved by comments provided by the participants. Publisher Copyright: © 2014 Elsevier B.V. All rights reserved.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

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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AN - SCOPUS:84944146735

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VL - 93

SP - 228

EP - 245

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

ER -

EM algorithms for estimating the Bernstein copula

Abstract

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