EM algorithms for estimating the Bernstein copula

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

Research output: Contribution to journalArticle

6 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 languageEnglish
Pages (from-to)228-245
Number of pages18
JournalComputational Statistics and Data Analysis
Volume93
DOIs
Publication statusPublished - 2016 Jan 1
Externally publishedYes

Fingerprint

Expectation-maximization Algorithm
Copula
Finite Mixture Distribution
Local Properties
Local Convergence
Multivariate Distribution
Statistics
Order Statistics
Convergence Properties
Asymptotic Properties
Estimator
Estimate

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

Cite this

EM algorithms for estimating the Bernstein copula. / Dou, Xiaoling; Kuriki, Satoshi; Lin, Gwo Dong; Richards, Donald.

In: Computational Statistics and Data Analysis, Vol. 93, 01.01.2016, p. 228-245.

Research output: Contribution to journalArticle

Dou, Xiaoling ; Kuriki, Satoshi ; Lin, Gwo Dong ; Richards, Donald. / EM algorithms for estimating the Bernstein copula. In: Computational Statistics and Data Analysis. 2016 ; Vol. 93. pp. 228-245.
@article{43d9dbcaf43d4e6aa714f94e83e40f42,
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.",
keywords = "Baker's distribution, Bernstein polynomial, Density estimation, Linear convergence, Order statistic, Ordered categorical data",
author = "Xiaoling Dou and Satoshi Kuriki and Lin, {Gwo Dong} and Donald Richards",
year = "2016",
month = "1",
day = "1",
doi = "10.1016/j.csda.2014.01.009",
language = "English",
volume = "93",
pages = "228--245",
journal = "Computational Statistics and Data Analysis",
issn = "0167-9473",
publisher = "Elsevier",

}

TY - JOUR

T1 - EM algorithms for estimating the Bernstein copula

AU - Dou, Xiaoling

AU - Kuriki, Satoshi

AU - Lin, Gwo Dong

AU - Richards, Donald

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.

KW - Baker's distribution

KW - Bernstein polynomial

KW - Density estimation

KW - Linear convergence

KW - Order statistic

KW - Ordered categorical data

UR - http://www.scopus.com/inward/record.url?scp=84944146735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944146735&partnerID=8YFLogxK

U2 - 10.1016/j.csda.2014.01.009

DO - 10.1016/j.csda.2014.01.009

M3 - Article

AN - SCOPUS:84944146735

VL - 93

SP - 228

EP - 245

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

ER -