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Expectation–maximization algorithm
About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.
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TL;DR: In this paper, the authors discuss the usefulness of simulation techniques in inference procedures, like maximum likelihood method, generalized moments method or pseudo maximum likelihood methods, from the point of view of consistency and asymptotic normality.
Abstract: In this paper we discuss the usefulness, for models with heterogeneity, of simulation techniques in inference procedures, like maximum likelihood method, generalized moments method or pseudo maximum likelihood methods. These proce dures are studied from the point of view of consistency, asymptotic normality, convergence rates and possible asymptotic bias. We carefully distinguish the case where the simulations are different for all the observations from the case where they are identical. Inference fondee sur des simulations dans des modeles avec heterogeneite
105 citations
TL;DR: The identifiability property of the MTIWD is proved and the estimates of the unknown parameters via the EM Algorithm are obtained.
105 citations
TL;DR: This paper introduces a novel hidden Markov model where the hidden state distributions are considered to be finite mixtures of multivariate Student's t-densities, and derives an algorithm for the model parameters estimation under a maximum likelihood framework, assuming full, diagonal, and factor-analyzed covariance matrices.
Abstract: Hidden Markov (chain) models using finite Gaussian mixture models as their hidden state distributions have been successfully applied in sequential data modeling and classification applications. Nevertheless, Gaussian mixture models are well known to be highly intolerant to the presence of untypical data within the fitting data sets used for their estimation. Finite Student's t-mixture models have recently emerged as a heavier-tailed, robust alternative to Gaussian mixture models, overcoming these hurdles. To exploit these merits of Student's t-mixture models in the context of a sequential data modeling setting, we introduce, in this paper, a novel hidden Markov model where the hidden state distributions are considered to be finite mixtures of multivariate Student's t-densities. We derive an algorithm for the model parameters estimation under a maximum likelihood framework, assuming full, diagonal, and factor-analyzed covariance matrices. The advantages of the proposed model over conventional approaches are experimentally demonstrated through a series of sequential data modeling applications.
105 citations
TL;DR: For a class of multivariate elliptically contoured distributions, the maximum likelihood estimators of the mean vector and covariance matrix were found under certain conditions in this article, and the likelihood-ratio criteria were obtained for the same form as in the normal case.
Abstract: For a class of multivariate elliptically contoured distributions the maximum-likelihood estimators of the mean vector and covariance matrix are found under certain conditions. Likelihood-ratio criteria are obtained for a class of null hypotheses. These have the same form as in the normal case.
105 citations
TL;DR: A new and computationally efficient forward-backward algorithm is proposed for HSMM with missing observations and multiple observation sequences, and the required computational amount for the forward and backward variables is reduced to O(D), where D is the maximum allowed duration in a state.
105 citations