EM algorithm for estimating the Bernstein copula

2016 Fiscal Year Final Research Report

• Project/Area Number: 26730024
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: Waseda University
• Principal Investigator: Dou Xiaoling 早稲田大学, 理工学術院, 助教 (10516868)
• Research Collaborator: KURIKI Satoshi 統計数理研究所, 数理推論研究系, 教授 ; LIN Gwo Dong Academia Sinica, The Institute of Statistical Science, Research Fellow ; RICHARDS Donald Pennsylvania State University, Department of Statistics, Professor
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 多変量分布推定 / 順序統計量 / 周辺分布 / 経験分布関数 / コピュラ / 有限混合分布 / EMアルゴリズム / カーネル密度推定

Outline of Final Research Achievements

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.

Free Research Field

分布理論