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 language | English |
|---|---|
| Pages (from-to) | 228-245 |
| Number of pages | 18 |
| Journal | Computational Statistics and Data Analysis |
| Volume | 93 |
| DOIs | |
| Publication status | Published - 2016 Jan 1 |
| Externally published | Yes |
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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 journal › Article
}
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
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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 -