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Generalized semiparametrically structured mixed models

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2004年第4期46卷 777-800页

作者： Tutz, G Univ Munich D-80799 Munich Germany

Generalized linear mixed models are a common tool in statistics which extends generalized linear models to situations where data are hierarchically clustered or correlated. It is shown that the simple but often inadequate restriction to a linear form of the predictor variables may be dropped. A class of semiparametrically structured models is proposed in which the predictor decomposes into components that may be given by a parametric term, an additive form of unspecified smooth functions of covariates, varying-coefficient terms or terms which vary smoothly (or not) across the repetitions in a repeated measurement design. The class of models is explicitly designed as an extension of multivariate generalized mixed linear models such that ordinal responses may be treated within this framework. The modelling of smooth effects is based on basis functions like e.g. B-splines or radial basis functions. For the estimation of parameters a penalized marginal likelihood approach is proposed which may be based on integration techniques like Gauss-Hermite quadrature but may as well be used within the more recently developed nonparametric maximum likelihood approaches. For the maximization of the penalized marginal likelihood the em-algorithm is adapted. It is shown that this extended em-algorithm shares the property of monotonicity with the usual em-algorithm. Moreover, an adequate form of cross-validation is developed and shown to work satisfactorily. Various examples demonstrate the flexibility of the class of models. (C) 2003 Elsevier B.V. All rights reserved.

关键词： generalized linear mixed models generalized semiparametrically structured mixed models em-algorithm ordinal mixed models cross-validation nonparametric maximum likelihood penalized marginal likelihood

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An approach to non-homogenous phase-type distributions through multiple cut-points

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QUALITY ENGINEERING 2023年第4期35卷 619-638页

作者： Ruiz-Castro, Juan Eloy Acal, Christian Roldan, Juan B. Univ Granada Dept Stat & OR Granada Spain Univ Granada IMAG Granada Spain Univ Granada Dept Elect & Comp Technol Granada Spain

A new class of distributions based on phase-type distributions is introduced in the current paper to model lifetime data in the field of reliability analysis. This one is the natural extension of the distribution proposed by Acal et al. (One cut-point phase-type distributions in reliability. An application to resistive random access memories. Mathematics 9(21):2734, 2021) for more than one cut-point. Multiple interesting measures such as density function, hazard rate or moments, among others, were worked out both for the continuous and discrete case. Besides, a new em-algorithm is provided to estimate the parameters by maximum likelihood. The results have been implemented computationally in R and simulation studies reveal that this new distribution reduces the number of parameters to be estimated in the optimization process and, in addition, it improves the fitting accuracy in comparison with the classical phase-type distributions, especially in heavy tailed distributions. An application is presented in the context of resistive memories with a new set of electron devices for nonvolatile memory circuits. In particular, the voltage associated with the resistive switching processes that control the internal behavior of resistive memories has been modeled with this new distribution to shed light on the physical mechanisms behind the operation of these memories.

关键词： Markov processes phase-type distributions multiple cut-points modeling em-algorithm simulation resistive random access memory (RRAM)

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Nonparametric estimation from length-biased data under competing risks

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2007年第5期51卷 2653-2669页

作者： de Una-Alvarez, Jacobo Rodriguez-Casal, Alberto Univ Vigo Dept Stat & Operat Res Vigo 36310 Spain

A new model for cross-sectional lifetime data is presented. The model is based on the length-bias assumption, and it is adapted to situations in which several types of censoring may occur. The NPMLE of the survival function is derived. An em-algorithm to approximate the NPMLE is devised. The performance of the introduced estimator is investigated through simulations. A real set of data collected as part of a study on unemployment duration in Spain is used for illustration purposes. (c) 2006 Elsevier B.V. All rights reserved.

关键词： censored data cross-section em-algorithm nonparametric likelihood self-consistency

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Detecting shocks: Outliers and breaks in time series

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JOURNAL OF ECONOMETRICS 1997年第2期80卷 387-422页

作者： Atkinson, AC Koopman, SJ Shephard, N UNIV OXFORD NUFFIELD COLL OXFORD OX1 1NFENGLAND TILBURG UNIV CTR NL-5000 LE TILBURGNETHERLANDS UNIV LONDON LONDON SCH ECON & POLIT SCI DEPT STATLONDON WC2A 2AEENGLAND

A single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares, An equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question, Similarly, for unobserved components or structural time-series models, the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter, such as trend or level changes. Because such time-series models contain more than one variance, the effect of the intervention is measured by the change in individual variances. We examine the effect on the estimated parameters of moving various kinds of intervention along the series, The horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing. Interpretation of the resulting time-series plots of diagnostics is aided by simulation envelopes. Our procedures, illustrated with four example, permit keen insights into the fragility of inferences to specific shocks, such as outliers and level breaks. Although the emphasis is mostly on parameter estimation, forecast are also considered. Possible extensions include seasonal adjustment and detrending of series. (C) 1997 Elsevier Science S.A.

关键词： added variable deletion methods diagnostics dynamic linear mode em-algorithm fragility Kalman filter Monte-Carlo test outlier score test shocks simulation envelope structural change structural time-series model unobserved components model

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ANALYSIS OF GRAY-LEVEL HISTOGRAMS BY USING STATISTICAL-METHODS FOR MIXTURES OF DISTRIBUTIONS

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PATTERN RECOGNITION LETTERS 1993年第7期14卷 585-590页

作者： JANSEN, RC REININK, K VANDERHEIJDEN, GWAM Centre for Plant Breeding and Reproduction Research (CPRO-DLO) P.O. Box 16 6700 AA Wageningen Netherlands

An automatic procedure to estimate proportions of components from grey level histograms is proposed. This procedure is based on statistical methods for parameter estimation in mixtures of normal distributions by maximum likelihood. The major advantage is that proportions of components can be estimated properly even when the grey level distributions of the components overlap considerably.

关键词： em-algorithm GRAY LEVEL HISTOGRAM IMAGE ANALYSIS MAXIMUM LIKELIHOOD MIXTURES OF LOGNORMAL DISTRIBUTIONS ROBUST PARAMETER ESTIMATION

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Progressive Type-II censoring and coherent systems

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NAVAL RESEARCH LOGISTICS 2015年第6期62卷 512-530页

作者： Cramer, Erhard Navarro, Jorge Rhein Westfal TH Aachen Inst Stat Dept Math D-52056 Aachen Germany Univ Murcia Fac Matemat Dept Stat & Operat Res E-30100 Murcia Spain

A new connection between the distribution of component failure times of a coherent system and (adaptive) progressively Type-II censored order statistics is established. Utilizing this property, we develop inferential procedures when the data is given by all component failures until system failure in two scenarios: In the case of complete information, we assume that the failed component is also observed whereas in the case of incomplete information, we have only information about the failure times but not about the components which have failed. In the first setting, we show that inferential methods for adaptive progressively Type-II censored data can directly be applied to the problem. For incomplete information, we face the problem that the corresponding censoring plan is not observed and that the available inferential procedures depend on the knowledge of the used censoring plan. To get estimates for distributional parameters, we propose maximum likelihood estimators which can be obtained by solving the likelihood equations directly or via an Expectation-Maximization-algorithm type procedure. For an exponential distribution, we discuss also a linear estimator to estimate the mean. Moreover, we establish exact distributions for some estimators in the exponential case which can be used, for example, to construct exact confidence intervals. The results are illustrated by a five component bridge system. (c) 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 512-530, 2015

关键词： progressive Type-II censoring progressive censoring with random removals coherent systems likelihood inference em-algorithm bridge system signature

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Mixture-based clustering for the ordered stereotype model

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 93卷 46-75页

作者： Fernandez, D. Arnold, R. Pledger, S. Victoria Univ Wellington Sch Math Stat & Operat Res Wellington 6140 New Zealand

Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. Recently a group of likelihood-based finite mixture models for a data matrix with binary or count data, using basic Bernoulli or Poisson building blocks has been developed. This is extended and establishes likelihood-based multivariate methods for a data matrix with ordinal data which applies fuzzy clustering via finite mixtures to the ordered stereotype model. Model-fitting is performed using the expectation-maximization (em) algorithm, and a fuzzy allocation of rows, columns, and rows and columns simultaneously to corresponding clusters is obtained. A simulation study is presented which includes a variety of scenarios in order to test the reliability of the proposed model. Finally, the results of the application of the model in two real data sets are shown. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Biclustering Cluster analysis Dimension reduction em-algorithm Finite mixture model Fuzzy clustering Likert scale Ordinal data Stereotype model

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Optimized multiple linear mappings for single image super-resolution

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OPTICS COMMUNICATIONS 2017年 404卷 169-176页

作者： Zhang, Kaibing Li, Jie Xiong, Zenggang Liu, Xiuping Gao, Xinbo Xian Polytech Univ Coll Elect & Informat Xian 710048 Shaanxi Peoples R China Xidian Univ Sch Elect Engn Xian 710071 Shaanxi Peoples R China Hubei Engn Univ Sch Comp & Informat Sci Xiaogan 432000 Peoples R China

Learning piecewise linear regression has been recognized as an effective way for example learning-based single image super-resolution (SR) in literature. In this paper, we employ an expectation-maximization (em) algorithm to further improve the SR performance of our previous multiple linear mappings (MLM) based SR method. In the training stage, the proposed method starts with a set of linear regressors obtained by the MLM-based method, and then jointly optimizes the clustering results and the low- and high-resolution subdictionary pairs for regression functions by using the metric of the reconstruction errors. In the test stage, we select the optimal regressor for SR reconstruction by accumulating the reconstruction errors of m-nearest neighbors in the training set. Thorough experimental results carried on six publicly available datasets demonstrate that the proposed SR method can yield high-quality images with finer details and sharper edges in terms of both quantitative and perceptual image quality assessments. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Example learning em-algorithm Image super-resolution (SR) Multiple linear mappings

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Cluster validity indices for mixture hazards regression models

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MATHemATICAL BIOSCIENCES AND ENGINEERING 2020年第2期17卷 1616-1636页

作者： Chang, Yi-Wen Lu, Kang-Ping Chang, Shao-Tung Natl Taiwan Normal Univ Dept Math Taipei Taiwan Natl Taichung Univ Sci & Technol Dept Appl Stat Taichung Taiwan

In the analysis of survival data, the problems of competing risks arise frequently in medical applications where individuals fail from multiple causes. Semiparametric mixture regression models have become a prominent approach in competing risks analysis due to their flexibility and easy interpretation of resultant estimates. The literature presents several semiparametric methods on the estimations for mixture Cox proportional hazards models, but fewer works appear on the determination of the number of model components and the estimation of baseline hazard functions using kernel approaches. These two issues are important because both incorrect number of components and inappropriate baseline functions can lead to insufficient estimates of mixture Cox hazard models. This research thus proposes four validity indices to select the optimal number of model components based on the posterior probabilities and residuals resulting from the application of an em-based algorithm on a mixture Cox regression model. We also introduce a kernel approach to produce a smooth estimate of the baseline hazard function in a mixture model. The effectiveness and the preference of the proposed cluster indices are demonstrated through a simulation study. An analysis on a prostate cancer dataset illustrates the practical use of the proposed method.

关键词： mixture regression model Cox proportional hazards model em-algorithm kernel estimator validity indices

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Generalized exponential-power series distributions

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2012年第12期56卷 4047-4066页

作者： Mahmoudi, Eisa Jafari, Ali Akbar Yazd Univ Dept Stat Yazd Iran

In this paper, we introduce the generalized exponential-power series (GEPS) class of distributions, which is obtained by compounding generalized exponential and power series distributions. The compounding procedure follows the same way as previously carried out in introducing the complementary exponential-geometric (CEG) and the two-parameter Poisson-exponential (PE) lifetime distributions. This new class of distributions contains several lifetime models such as: CEG, PE, generalized exponential-binomial (GEB), generalized exponential-Poisson (GEP), generalized exponential-geometric (GEG) and generalized exponential-logarithmic (GEL) distributions as special cases. The hazard function of the GEPS distributions can be increasing, decreasing or bathtub shaped among others. We obtain several properties of the GEPS distributions such as moments, maximum likelihood estimation procedure via an em-algorithm and inference for a large sample. Special distributions are studied in some detail. At the end, in order to show the flexibility and potentiality of the new class of distributions, we demonstrate applications of two real data sets. (C) 2012 Elsevier B.V. All rights reserved.

关键词： em-algorithm Generalized exponential distribution Maximum likelihood estimation Power series distributions

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