Recent trends in education aid: Towards a classification of policies: Lene Buchert, Paris, UNESCO/International Institute for Educational Planning, 1995, 62pp

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.