EM algorithms for estimating the Bernstein copula

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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
Publication statusPublished - 2016 Jan 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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