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Mixture transition distribution (MTD) modeling of heteroscedastic time series

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2003年第3-4期41卷 399-411页

作者： Berchtold, A Univ Lausanne Inst Appl Math SSP CH-1015 Lausanne Switzerland

Time series presenting non-Gaussian features such as heteroscedasticity or sudden bursts of activity play a central role in many fields including finance, insurance, and seismology. The heteroscedastic mixture transition distribution (HMTD) model, which generalizes several specifications previously proposed in the statistical literature, is a new model especially designed to handle series of this kind. By allowing the standard deviation of each component to be a function of the past of the observed process, a better modeling of the conditional probability distribution function of future observations is obtained. A numerical example shows that the HMTD can perform better than standard models such as ARMA and GARCH. Different issues related to the numerical estimation of mixture models are also discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： time series heteroscedasticity mixture HMTD gem algorithm degencrescence of the log-likelihood

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Mixture-model-based signal denoising

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2007年第1期1卷 39-51页

作者： Same, Allou Oukhellou, Latifa Come, Etienne Aknin, Patrice Inst Natl Rech Transports & Secur INRETS F-94114 Arcueil France Univ Paris 12 CERTES F-94100 Creteil France

This paper proposes a new signal denoising methodology for dealing with asymmetrical noises. The adopted strategy is based on a regression model where the noise is supposed to be additive and distributed following a mixture of Gaussian densities. The parameters estimation is performed using a Generalized EM (gem) algorithm. Experimental studies on simulated and real signals in the context of a diagnosis application in the railway domain reveal that the proposed approach performs better than the least-squares and wavelets methods.

关键词： Denoising Asymmetrical noise Regression Gaussian mixture model EM algorithm gem algorithm

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Predictors with measurement error in mixtures of polynomial regressions

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COMPUTATIONAL STATISTICS 2023年第1期38卷 373-401页

作者： Fang, Xiaoqiong Chen, Andy W. Young, Derek S. Corp & Investment Bank JP Morgan Brooklyn NY USA Seattle Pacific Univ Sch Business Govt & Econ Seattle WA USA Univ Kentucky Dr Bing Zhang Dept Stat Lexington KY 40546 USA

There has been a substantial body of research on mixtures-of-regressions models that has developed over the past 20 years. While much of the recent literature has focused on flexible mixtures-of-regressions models, there is still considerable utility for imposing structure on the mixture components through fully parametric models. One feature of the data that is scantly addressed in mixtures of regressions is the presence of measurement error in the predictors. The limited existing research on this topic concerns the case where classical measurement error is added to the classic mixtures-of-linear-regressions model. In this paper, we consider the setting of mixtures of polynomial regressions where the predictors are subject to classical measurement error. Moreover, each component is allowed to have a different degree for the polynomial structure. We utilize a generalized expectation-maximization algorithm for performing maximum likelihood estimation. For estimating standard errors, we extend a semiparametric bootstrap routine that has been employed for mixtures of linear regressions without measurement error in the predictors. Numeric work, for practical reasons identified, is limited to estimating two-component models. We consider a likelihood ratio test for determining if there is a higher-degree polynomial term in one of the components. Model selection criteria are also highlighted as a way for determining an appropriate model. A simulation study and an application to the classic nitric oxide emissions data are provided.

关键词： Bootstrap Finite mixture models gem algorithm Model selection Regression calibration Surrogate data

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Convergence properties of the EM algorithm in constrained parameter spaces

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 1999年第3期27卷 639-648页

作者： Nettleton, D Univ Nebraska Dept Math & Stat Lincoln NE 68588 USA

The established general results on convergence properties of the EM algorithm require the sequence of EM parameter estimates to fall in the interior of the parameter space over which the likelihood is being maximized. This paper presents convergence properties of the EM sequence of likelihood values and parameter estimates in constrained parameter spaces for which the sequence of EM parameter estimates may converge to the boundary of the constrained parameter space contained in the interior of the unconstrained parameter space. Examples of the behavior of the EM algorithm applied to such parameter spaces are presented.

关键词： EM algorithm gem algorithm ECM algorithm AECM algorithm incomplete data inequality constraints order-restricted inference restricted maximum-likelihood estimate

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Zero-and-one-inflated Poisson regression model

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STATISTICAL PAPERS 2021年第2期62卷 915-934页

作者： Liu, Wenchen Tang, Yincai Xu, Ancha East China Normal Univ Sch Stat KLATASDS MOE Shanghai 200241 Peoples R China Wenzhou Univ Dept Math Wenzhou 325035 Zhejiang Peoples R China

In this paper, a zero-and-one-inflated Poisson (ZOIP) regression model is proposed. The maximum likelihood estimation (MLE) and Bayesian estimation for this model are investigated. Three estimation methods of the ZOIP regression model are obtained based on data augmentation method which is expectation-maximization (EM) algorithm, generalized expectation-maximization (gem) algorithm and Gibbs sampling respectively. A simulation study is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, an accidental deaths data set is analyzed to illustrate the practicability of the proposed method.

关键词： Zero-and-one-inflated Poisson regression model Data augmentation Gibbs sampling EM algorithm gem algorithm

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ON THE CONVERGENCE PROPERTIES OF THE EM algorithm

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ANNALS OF STATISTICS 1983年第1期11卷 95-103页

作者： WU, CFJ

Two convergence aspects of the EM algorithm are studied: (i) does the EM algorithm find a local maximum or a stationary value of the (incomplete-data) likelihood function? (ii) does the sequence of parameter estimates generated by EM converge? Several convergence results are obtained under conditions that are applicable to many practical situations. Two useful special cases are: (a) if the unobserved complete-data specification can be described by a curved exponential family with compact parameter space, all the limit points of any EM sequence are stationary points of the likelihood function; (b) if the likelihood function is unimodal and a certain differentiability condition is satisfied, then any EM sequence converges to the unique maximum likelihood estimate. A list of key properties of the algorithm is included.

关键词： 62F10 90C30 curved exponential family EM algorithm gem algorithm incomplete data maximum likelihood estimate

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On the Convergence of theEMalgorithm

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Journal of the Royal Statistical Society: Series B (Statistical Methodology) 1983年第1期45卷 47-50页

作者： Russell A. Boyles Lawrence Livermore National Laboratory USA

An example is given showing that a sequence generated by a gem algorthm need not converge under the conditions stated in Dempster et al., (1977). Two general convergence results are presented which suggest that in practice a gem sequence will converge to a compact connected set of local maxima of the likelihood function; this limit set may or may not consist of a single point.

关键词： maximum likelihood em algorithm gem algorithm incomplete data

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