TY - JOUR
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.
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
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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 -