EM algorithm using overparameterization for the multivariate skew-normal distribution

Toshihiro Abe, Hironori Fujisawa, Takayuki Kawashima and Christophe Ley

Econometrics and Statistics, 2021, vol. 19, issue C, 151-168

Abstract: 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.

Keywords: EM algorithm; Maximum likelihood estimate; Multivariate skew-normal distribution; Momentum; Overparameterization (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:19:y:2021:i:c:p:151-168

DOI: 10.1016/j.ecosta.2021.03.003

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