EM algorithms for estimating the Bernstein copula

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

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 (US)
Pages (from-to)228-245
Number of pages18
JournalComputational Statistics and Data Analysis
StatePublished - Jan 1 2016

All Science Journal Classification (ASJC) codes

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


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