EM algorithm; Maximum likelihood estimate; Momentum; Multivariate skew-normal distribution; Overparameterization; Statistics and Probability; Economics and Econometrics; Statistics, Probability and Uncertainty
Abstract :
[en] A stochastic representation with a latent variable often enables us to make an EM algorithm to obtain the maximum likelihood estimate. The skew-normal distribution has such a simple stochastic representation with a latent variable, and consequently one expects to have a convenient EM algorithm. However, even for the univariate skew-normal distribution, existing EM algorithms constructed using a stochastic representation require a solution of a complicated estimating equation for the skewness parameter, making it difficult to extend such an idea to the multivariate skew-normal distribution. A stochastic representation with overparameterization is proposed, which has not been discussed yet. The approach allows the construction of an efficient EM algorithm in a closed form, which can be extended to a mixture of multivariate skew-normal distributions. The proposed EM algorithm can be regarded as an accelerated version with momentum (which is known as an acceleration technique of the algorithm in optimization) of a recently proposed EM algorithm. The novel EM algorithm is applied to real data and compared with the command msn.mle from the R package sn.
Disciplines :
Mathematics Business & economic sciences: Multidisciplinary, general & others
Author, co-author :
Abe, Toshihiro ; Faculty of Economics, Hosei University, Tokyo, Japan
Fujisawa, Hironori; The Institute of Statistical Mathematics, Tokyo, Japan ; Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan
Kawashima, Takayuki; Department of Mathematical and Computing Science, Tokyo Institute of Technology, Tokyo, Japan ; Center for Advanced Intelligence Project, RIKEN, Tokyo, Japan
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Gent, Belgium
External co-authors :
yes
Language :
English
Title :
EM algorithm using overparameterization for the multivariate skew-normal distribution
Toshihiro Abe was supported in part by JSPS KAKENHI [grant numbers 19K11869 and 19KK0287]; and Nanzan University Pache Research Subsidy I-A-2 for the 2020 academic year.Toshihiro Abe was supported in part by JSPS KAKENHI [grant numbers 19K11869 and 19KK0287]. Hironori Fujisawa was supported in part by JSPS KAKENHI [grant number 17K00065]. Takayuki Kawashima was supported in part by JSPS KAKENHI [grant numbers 19K24340 and 19H04071]. Christophe Ley is supported by the FWO Krediet aan Navorsers grant with reference number 1510391N.
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