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stochastic em algorithm of a finite mixture model from hurdle Poisson distribution with missing responses

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2016年第20期45卷 5918-5932页

作者： Fu, Ying-zi Kunming Sci & Technol Univ Fac Sci Kunming 650500 Yunnan Province Peoples R China

In this article, a finite mixture model of hurdle Poisson distribution with missing outcomes is proposed, and a stochastic em algorithm is developed for obtaining the maximum likelihood estimates of model parameters and mixing proportions. Specifically, missing data is assumed to be missing not at random (MNAR)/non ignorable missing (NINR) and the corresponding missingness mechanism is modeled through probit regression. To improve the algorithm efficiency, a stochastic step is incorporated into the E-step based on data augmentation, whereas the M-step is solved by the method of conditional maximization. A variation on Bayesian information criterion (BIC) is also proposed to compare models with different number of components with missing values. The considered model is a general model framework and it captures the important characteristics of count data analysis such as zero inflation/deflation, heterogeneity as well as missingness, providing us with more insight into the data feature and allowing for dispersion to be investigated more fully and correctly. Since the stochastic step only involves simulating samples from some standard distributions, the computational burden is alleviated. Once missing responses and latent variables are imputed to replace the conditional expectation, our approach works as part of a multiple imputation procedure. A simulation study and a real example illustrate the usefulness and effectiveness of our methodology.

关键词： Finite mixture model Hurdle Poisson distribution Missing data Model selection stochastic em algorithm

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stochastic em algorithm for doubly interval-censored data

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BIOSTATISTICS 2013年第4期14卷 766-778页

作者： Dejardin, David Lesaffre, emmanuel KULeuven Interuniv Inst Biostat & Stat Bioinformat B-3000 Louvain Belgium Univ Hasselt B-3000 Louvain Belgium Bristol Myers Squibb Global Biometr Sci B-1420 Braine Lalleud Belgium Erasmus MC Dept Biostat NL-3015 CE Rotterdam Netherlands

In clinical trials, it is frequently of interest to estimate the time between the onset of two events (e. g. duration of response in oncology). Here, we consider the case where subjects are assessed at fixed visits but the initial event and the terminating event occur in between visits. This type of data, called doubly interval censored, is often analyzed with standard survival techniques, assuming either that the survival time (between initial and terminating event) is known exactly or is single interval censored. We introduce a motivating dataset in which the interest is to evaluate the impact of the treatment on the duration of response endpoint. We review the existing approaches and discuss their limitations with respect to the characteristics of our motivating dataset. Furthermore, we propose a stochastic em algorithm that overcomes the problems in the existing approaches. We show by simulations the finite sample properties of our approach.

关键词： Cox proportional hazard Doubly interval censored stochastic em algorithm

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A stochastic em algorithm for Progressively Censored Data Analysis

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QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL 2014年第5期30卷 711-722页

作者： Zhang, Mimi Ye, Zhisheng Xie, Min City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China Hong Kong Polytech Univ Dept Appl Math Hong Kong Hong Kong Peoples R China Natl Univ Singapore Dept Ind & Syst Engn Singapore 117548 Singapore

Progressive censoring technique is useful in lifetime data analysis. Simple approaches to progressive data analysis are crucial for its widespread adoption by reliability engineers. This study develops an efficient yet easy-to-implement framework for analyzing progressively censored data by making use of the stochastic em algorithm. On the basis of this framework, we develop specific stochastic em procedures for several popular lifetime models. These procedures are shown to be very simple. We then demonstrate the applicability and efficiency of the stochastic em algorithm by a fatigue life data set with proper modification and by a progressively censored data set from a life test on hard disk drives. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： stochastic em algorithm progressively censored data lifetime distribution

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An improved stochastic em algorithm for large-scale full-information item factor analysis

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BRITISH JOURNAL OF MATHemATICAL & STATISTICAL PSYCHOLOGY 2020年第1期73卷 44-71页

作者： Zhang, Siliang Chen, Yunxiao Liu, Yang Fudan Univ Shanghai Ctr Math Sci Shanghai Peoples R China London Sch Econ & Polit Sci Dept Stat London England Univ Maryland Dept Human Dev & Quantitat Methodol College Pk MD 20742 USA

In this paper, we explore the use of the stochastic em algorithm (Celeux & Diebolt (1985) Computational Statistics Quarterly, 2, 73) for large-scale full-information item factor analysis. Innovations have been made on its implementation, including an adaptive-rejection-based Gibbs sampler for the stochastic E step, a proximal gradient descent algorithm for the optimization in the M step, and diagnostic procedures for determining the burn-in size and the stopping of the algorithm. These developments are based on the theoretical results of Nielsen (2000, Bernoulli, 6, 457), as well as advanced sampling and optimization techniques. The proposed algorithm is computationally efficient and virtually tuning-free, making it scalable to large-scale data with many latent traits (e.g. more than five latent traits) and easy to use for practitioners. Standard errors of parameter estimation are also obtained based on the missing-information identity (Louis, 1982, Journal of the Royal Statistical Society, Series B, 44, 226). The performance of the algorithm is evaluated through simulation studies and an application to the analysis of the IPIP-NEO personality inventory. Extensions of the proposed algorithm to other latent variable models are discussed.

关键词： full-information item factor analysis Gibbs sampler multidimensional item response theory proximal gradient descent rejection sampling stochastic em algorithm

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Asymptotic properties of a stochastic em algorithm for mixtures with censored data

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2010年第1期140卷 111-127页

作者： Svensson, Ingrid Sjostedt-de Luna, Sara Umea Univ Dept Stat S-90187 Umea Sweden Umea Univ Dept Math & Math Stat S-90187 Umea Sweden

Weak consistency and asymptotic normality is shown for a stochastic em algorithm for censored data from a mixture of distributions under lognormal assumptions. The asymptotic properties hold for all parameters of the distributions, including the mixing parameter. In order to make parameter estimation meaningful it is necessary to know that the censored mixture distribution is identifiable. General conditions under which this is the case are given. The stochastic em algorithm addressed in this paper is used for estimation of wood fibre length distributions based on optically measured data from cylindric wood samples (increment cores). (C) 2009 Elsevier B.V. All rights reserved.

关键词： Censoring Fibre length distribution Identifiability Increment core Mixture stochastic em algorithm

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A stochastic em algorithm for Quantile and Censored Quantile Regression Models

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COMPUTATIONAL ECONOMICS 2018年第2期52卷 555-582页

作者： Yang, Fengkai Shandong Univ Sch Math Jinan 250100 Shandong Peoples R China Shandong Univ Sch Math & Stat Weihai 264209 Peoples R China

We proposed a stochastic em algorithm for quantile and censored quantile regression models in order to circumvent some limitations of the em algorithm and Gibbs sampler. We conducted several simulation studies to illustrate the performance of the algorithm and found that the procedure performs as better as the Gibbs sampler, and outperforms the em algorithm in uncensored situation. Finally we applied the methodology to the classical Engel food expenditure data and the labour supply data with left censoring, finding that the Sem algorithm behaves more satisfying than the Gibbs sampler does.

关键词： stochastic em algorithm Quantile regression Censored quantile regression Gibbs sampling

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Likelihood analysis and stochastic em algorithm for left truncated right censored data and associated model selection from the Lehmann family of life distributions

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JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2021年第2期4卷 1019-1048页

作者： Mitra, Debanjan Kundu, Debasis Balakrishnan, Narayanaswamy Indian Inst Management Udaipur Udaipur 313001 Rajasthan India Indian Inst Technol Kanpur Kanpur 208016 Uttar Pradesh India McMaster Univ Hamilton ON L8S 4K1 Canada

The Lehmann family of distributions includes Weibull, Gompertz, and Lomax models as special cases, all of which are quite useful for modeling lifetime data. Analyses of left truncated right censored data from the Lehmann family of distributions are carried out in this article. In particular, the special cases of Weibull, Gompertz, and Lomax distributions are considered. Maximum likelihood estimates of the model parameters are obtained. The steps of the stochastic expectation maximization algorithm are developed in this context. Asymptotic confidence intervals for the model parameters are constructed using the missing information principle and two parametric bootstrap approaches. Through extensive Monte Carlo simulations, performances of the inferential methods are examined. The effect of model misspecification is also assessed within this family of distributions through simulations. As it is quite important to select a suitable model for a given data, a study of model selection based on left truncated right censored data is carried out through extensive Monte Carlo simulations. Two examples based on real datasets are provided for illustrating the models and methods of inference discussed here.

关键词： Maximum likelihood estimators stochastic em algorithm Left truncation Right censoring Weibull distribution Gompertz distribution Lomax distribution Missing information principle Asymptotic confidence intervals Bootstrap method Model selection

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Asymptotic results for a stationary random process generated by the stochastic em algorithm in mixture analyses

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JOURNAL OF STATISTICS & MANAGemENT SYSTemS 2018年第2期21卷 251-260页

作者： Polymenis, Athanase Univ Patras Dept Econ Univ Campus Rio Rion 26504 Greece

Implementing the stochastic em (or Sem) algorithm for parameter estimation in finite mixture models yields a random process which is normally distributed AR(1) as the sample size tends to infinity. The normal distribution underlying this process follows from a regularity assumption pertaining to theory concerning Sem. In the present paper we consider a centred version {X-i} of this process and focus on the particular case where this is generated from the stationary state of Sem, denoted as process {X-(i)}. We study distribution properties of Sigma(n)(i=1) X-(i) / root n as n tends to infinity without assuming a normal distribution for {X-(i)}. To this end a multivariate central limit theorem is shown to apply and relationship between the variance of Sigma(n)(i=1) X-(i) / root n as n tends to infinity and that of Sigma(r)(i=1) X-i / root r for r sufficiently large is established.

关键词： mixture model stochastic em algorithm asymptotically stationary process asymptotic distribution

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An em and a stochastic Version of the em algorithm for Nonparametric Hidden Semi-Markov Models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2010年第2期39卷 240-261页

作者： Malefaki, Sonia Trevezas, Samis Limnios, Nikolaos UTC Lab Math Appl Compiegne Compiegne France

The Hidden semi-Markov models (HSMMs) were introduced to overcome the constraint of a geometric sojourn time distribution for the different hidden states in the classical hidden Markov models. Several variations of HSMMs were proposed that model the sojourn times by a parametric or a nonparametric family of distributions. In this article, we concentrate our interest on the nonparametric case where the duration distributions are attached to transitions and not to states as in most of the published papers in HSMMs. Therefore, it is worth noticing that here we treat the underlying hidden semi-Markov chain in its general probabilistic structure. In that case, Barbu and Limnios (2008) proposed an Expectation-Maximization (em) algorithm in order to estimate the semi-Markov kernel and the emission probabilities that characterize the dynamics of the model. In this article, we consider an improved version of Barbu and Limnios' em algorithm which is faster than the original one. Moreover, we propose a stochastic version of the em algorithm that achieves comparable estimates with the em algorithm in less execution time. Some numerical examples are provided which illustrate the efficient performance of the proposed algorithms.

关键词： em algorithm Hidden semi-Markov models Maximum likelihood estimation stochastic em algorithm

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A non linear mixed effects model of plant growth and estimation via stochastic variants of the em algorithm

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2016年第6期45卷 1643-1669页

作者： Baey, Charlotte Trevezas, Samis Cournede, Paul-Henry Ecole Cent Paris Lab Math Appl Syst F-92290 Chatenay Malabry France

There is a strong genetic variability among plants, even of the same variety, which, combined with the locally varying environmental conditions in a given field, can lead to the development of highly different neighboring plants. This is one of the reasons why population-based methods for modeling plant growth are of great interest. GreenLab is a functional-structural plant growth model which has already been shown to be successful in describing plant growth dynamics primarily at individual level. In this study, we extend its formulation to the population level. In order to model the deviations from some fixed but unknown important biophysical and genetic parameters we introduce random effects. The resulting model can be cast into the framework of non linear mixed models, which can be seen as particular types of incomplete data models. A stochastic variant of an em-type algorithm (expectation-maximization) is generally needed to perform maximum likelihood estimation for this type of models. Under some assumptions, the complete data distribution belongs to a subclass of the exponential family of distributions for which the M-step can be solved explicitly. In such cases, the interest is focused on the best approximation of the E-step by competing simulation methods. In this direction, we propose to compare two commonly used stochastic algorithms: the Monte-Carlo em (MCem) and the SAem algorithm. The performances of both algorithms are compared on simulated data, and an application to real data from sugar beet plants is also given.

关键词： MCMC methods Non linear mixed effects model Plant growth model stochastic em algorithm Sugar beet plant 62F10 65C05

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