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International Conference on Numerical Analysis and Applied Mathematics (ICNAAM)

作者： Gorshenin, Andrey K. Russian Acad Sci Inst Informat Problems MIREA Fac Informat Technol Moscow Russia

ISBN: (纸本)9780735412873

The paper discusses the main ideas of an implementation of em-type algorithms for computing on the graphics processors and the application for the probabilistic models based on the Cox processes. An example of the GPU's adapted MATLAB source code for the finite normal mixtures with the expectation-maximization matrix formulas is given. The testing of computational efficiency for GPU vs CPU is illustrated for the different sample sizes.

关键词： GPU CPU matrices em-type algorithms stochastic models

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Inference and diagnostics for censored linear regression model with skewed generalized t distribution

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JOURNAL OF APPLIED STATISTICS 2025年第2期52卷 477-508页

作者： Lian, Chengdi Rong, Yaohua Liang, Jinwen Guan, Ruijie Cheng, Weihu Beijing Univ Technol Sch Math Stat & Mech 100 Pingleyuan Beijing Peoples R China

In recent years, some interested data can be recorded only if the values fall within an interval range, and the responses are often subject to censoring. Attempting to perform effective statistical analysis with censored, especially heavy-tailed and asymmetric data, can be difficult. In this paper, we develop a novel linear regression model based on the proposed skewed generalized t distribution for censored data. The likelihood-based inference and diagnostic analysis are established using the Expectation/Conditional Maximization Either algorithm in conjunction with smoothing approximate functions. We derive relevant measures to perform global influence for this novel model and develop local influence analysis based on the conditional expectation of the complete-data log-likelihood function. Some useful perturbation schemes are discussed. We illustrate the finite sample performance and the robustness of the proposed method by simulation studies. The proposed model is compared with other procedures based on a real dataset, and a sensitivity analysis is also conducted.

关键词： Censored regression model em-type algorithms influence analysis skewed generalized t distribution residual analysis

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Bounded data modeling using logit-skew-normal mixtures

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STATISTICAL PAPERS 2025年第3期66卷 1-21页

作者： Mahdavi, Abbas Contreras-Reyes, Javier E. Vali e Asr Univ Rafsanjan Dept Stat Rafsanjan Iran Univ Las Amer Fac Ingn & Negocios Inst Matemat Fis & Estadist 7 Norte 1348 Vina Del Mar Chile

Bounded data on (0, 1) have often been modelled in several real-world applications using several distributions. However, these studies lack addressing skewness, kurtosis and heavy-tailed properties in observations. This study presents a novel skew-normal type distribution defined within a bounded interval, which is derived by integrating the structures of skew-normal distributions and the logit function. With its extended skewness and bounded properties, the proposed model provides a versatile and suitable solution for modeling rates and proportions. We have developed an em-type algorithm to accurately estimate the model parameters and its finite mixtures. To illustrate the effectiveness of our approach, we conducted experiments that included two simulation studies and an analysis of real data. The results highlight the flexibility and accuracy of our proposed model in comparison to traditional mixture models.

关键词： em-type algorithms Mixture models Bounded distributions Logit-normal distribution Skew-normal distribution

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Finite mixture of regression models for censored data based on the skew-t distribution

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COMPUTATIONAL STATISTICS 2024年第7期39卷 3695-3726页

作者： Park, Jiwon Dey, Dipak K. Lachos, Victor H. Univ Connecticut Dept Stat Storrs CT 06269 USA

Finite mixture models have been widely used to model and analyze data from heterogeneous populations. In practical scenarios, these types of data often confront upper and/or lower detection limits due to the constraints imposed by experimental apparatuses. Additional complexity arises when measures of each mixture component significantly deviate from the normal distribution, manifesting characteristics such as multimodality, asymmetry, and heavy-tailed behavior, simultaneously. This paper introduces a flexible model tailored for censored data to address these intricacies, leveraging the finite mixture of skew-t distributions. An Expectation Conditional Maximization Either (ECME) algorithm, is developed to efficiently derive parameter estimates by iteratively maximizing the observed data log-likelihood function. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of truncated skew-t distributions. Moreover, a method based on general information principles is presented for approximating the asymptotic covariance matrix of the estimators. Results obtained from the analysis of both simulated and real datasets demonstrate the proposed method's effectiveness.

关键词： Censored regression em-type algorithms Finite mixture models Skew-t distribution Truncated distributions

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Regression modeling of censored data based on compound scale mixtures of normal distributions

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BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS 2023年第2期37卷 282-312页

作者： Benites, Luis Zeller, Camila B. Bolfarine, Heleno Lachos, Victor H. Pontificia Univ Catolica Peru Dept Ciencias Lima Peru Univ Fed Juiz de Fora Dept Estat Juiz De Fora Brazil Univ Sao Paulo Dept Estat Butanta SP Brazil Univ Connecticut Dept Stat Storrs CT USA

In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibility, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analytically tractable and efficient em-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodology addressed in this paper is implemented in the R package CensMixReg.

关键词： Censored regression model em-type algorithms finite mixture models heavy-tails distributions limit of detection Tobit model

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Finite mixture modeling of censored and missing data using the multivariate skew-normal distribution

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2022年第3期16卷 521-557页

作者： de Alencar, Francisco H. C. Galarza, Christian E. Matos, Larissa A. Lachos, Victor H. Univ Estadual Campinas Dept Estat Campinas SP Brazil ESPOL Escuela Super Politecn Litoral Fac Ciencias Nat & Matemat Guayaquil Ecuador Univ Connecticut Dept Stat Storrs CT 06269 USA

Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the constraints of experimental apparatuses. Another complication arises when measures of each population depart significantly from normality, such as asymmetric behavior. For such data structures, we propose a robust model for censored and/or missing data based on finite mixtures of multivariate skew-normal distributions. This approach allows us to model data with great flexibility, accommodating multimodality and skewness, simultaneously, depending on the structure of the mixture components. We develop an analytically simple, yet efficient, em-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the truncated multivariate skew-normal distributions. Furthermore, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed method. The proposed algorithm and method are implemented in the new R package CensMFM.

关键词： Censored data Detection limit em-type algorithms Finite mixture models Multivariate skew-normal distribution Truncated distributions

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Maximum likelihood estimation for scale-shape mixtures of flexible generalized skew normal distributions via selection representation

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COMPUTATIONAL STATISTICS 2021年第3期36卷 2201-2230页

作者： Mahdavi, Abbas Amirzadeh, Vahid Jamalizadeh, Ahad Lin, Tsung-, I Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran Natl Chung Hsing Univ Inst Stat Taichung 402 Taiwan China Med Univ Dept Publ Hlth Taichung 404 Taiwan

A scale-shape mixtures of flexible generalized skew normal (SSMFGSN) distributions is proposed as a novel device for modeling asymmetric data. Computationally feasible em-type algorithms derived from the selection mechanism are presented to compute maximum likelihood (ML) estimates of SSMFGSN distributions. Some characterizations and probabilistic properties of the SSMFGSN distributions are also studied. Monte Carlo simulations show that the proposed estimating procedures can provide desirable asymptotic properties of the ML estimates and demand less computational burden in comparison with other existing algorithms based on convolution representations. The usefulness of the proposed methodology is illustrated by analyzing a real dataset.

关键词： Bessel function em-type algorithms Exponential-power distribution Scale-shape mixtures Skew-symmetric distribution Truncated normal distribution

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Heckman selection-t model: Parameter estimation via the em-algorithm

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JOURNAL OF MULTIVARIATE ANALYSIS 2021年 184卷 104737-104737页

作者： Lachos, Victor H. Prates, Marcos O. Dey, Dipak K. Univ Connecticut Dept Stat Storrs CT 06269 USA Univ Fed Minas Gerais Dept Estat BR-31270901 Belo Horizonte MG Brazil

The Heckman selection model is perhaps the most popular econometric model in the analysis of data with sample selection. The analyses of this model are based on the normality assumption for the error terms, however, in some applications, the distribution of the error term departs significantly from normality, for instance, in the presence of heavy tails and/or atypical observation. In this paper, we explore the Heckman selection-t model where the random errors follow a bivariate Student's-t distribution. We develop an analytically tractable and efficient em-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student's-t distributions. Simulation studies show the vulnerability of the Heckman selection-normal model, as well as the robustness aspects of the Heckman selection-t model. Two real examples are analyzed, illustrating the usefulness of the proposed methods. The proposed algorithms and methods are implemented in the new R package Heckmanem. (C) 2021 Elsevier Inc. All rights reserved.

关键词： em-type algorithms Heckman selection model Multivariate Student's-t Robustness

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Efficient algorithms for robust estimation in autoregressive regression models using Student's t distribution

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2020年第2期49卷 355-374页

作者： Nduka, Uchenna C. Iwueze, Iheanyi S. Nwogu, Elezar C. Univ Nigeria Dept Stat Nsukka Enugu State Nigeria Fed Univ Technol Owerri Dept Stat Owerri Imo State Nigeria

It is now a common knowledge that most data that occur in practice violate the assumption of normality. The Student's t distribution is not only a handy alternative to such a case but also possesses a structure that makes estimation easy via numerical computation. This paper focuses on maximum-likelihood estimation of the parameters of autoregressive regression model driven by Student's t distribution. em-type algorithms are utilized to iteratively obtain the maximum-likelihood estimates of the parameters of the model. The method's performance is compared with the method of modified maximum-likelihood estimation in simulations and real data analysis.

关键词： Autoregression em-type algorithms Known and Unknown degrees of freedom Outliers Student's t distribution

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A new mixture model on the simplex

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STATISTICS AND COMPUTING 2020年第4期30卷 749-770页

作者： Ongaro, Andrea Migliorati, Sonia Ascari, Roberto Univ Milano Bicocca DEMS Dept Econ Management & Stat Milan Italy

This paper is meant to introduce a significant extension of the flexible Dirichlet (FD) distribution, which is a quite tractable special mixture model for compositional data, i.e. data representing vectors of proportions of a whole. The FD model displays several theoretical properties which make it suitable for inference, and fairly easy to handle from a computational viewpoint. However, the rigid type of mixture structure implied by the FD makes it unsuitable to describe many compositional datasets. Furthermore, the FD only allows for negative correlations. The new extended model, by considerably relaxing the strict constraints among clusters entailed by the FD, allows for a more general dependence structure (including positive correlations) and greatly expands its applicative potential. At the same time, it retains, to a large extent, its good properties. em-type estimation procedures can be developed for this more complex model, including ad hoc reliable initialization methods, which permit to keep the computational issues at a rather uncomplicated level. Accurate evaluation of standard error estimates can be provided as well.

关键词： Proportion Dirichlet mixture em-type algorithms Multi-modality Compositional invariance

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