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Single-replicate longitudinal data analysis in the presence of multiple instrumental measurement errors

COMPUTERS & INDUSTRIAL ENGINEERING 2020年 141卷 106301-106301页

作者： Moazeni, Mehran Behbahani, Mohammad Khedmati, Majid Niaki, Seyed Taghi Akhavan Sharif Univ Technol Dept Ind Engn POB 11155-9414 Azadi Ave Tehran *** Iran

In this paper, a novel method as a combination of the expectation-maximization (em) algorithm and Variogram is proposed to decompose the longitudinal measurement errors in the absence of replications and the presence of multiple instrumental measurement errors. In the proposed method, multiple measurements are considered where the units are observed by several distinct instruments (gauges). The approach decouples the observed variance of the measurement model into the process and measurement system variances. In addition, it decomposes the variance of multiple instruments into the process and instrument variances. In the end, the proposed model is validated and tested based on simulated longitudinal data as well as a real case study related to the Framingham Heart study, measuring systolic blood pressure by multiple instruments. In addition, the robustness of the proposed method to the missing values, a common problem in longitudinal data, is demonstrated.

关键词： Longitudinal data Reproducibility Multiple instruments em-algorithm Variogram Missing values

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Use of finite mixture models with skew-t-normal Birnbaum- Saunders components in the analysis of wind speed: Case studies in Ontario, Canada

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RENEWABLE ENERGY 2020年 162卷 196-211页

作者： Mahbudi, Shahrbanoo Jamalizadeh, Ahad Farnoosh, Rahman Islamic Azad Univ Sci & Res Branch Dept Stat Tehran Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran Univ Sci & Technol Sch Math Tehran Iran

The probabilistic distribution of wind speed is critical information required in evaluating wind resources, designing wind farms, and mitigating the possible risks in wind power expansion. Various distributions have been used in the research literature to estimate wind speed distribution. In this paper, we propose a flexible family of mixture distributions, whose elements are convex linear combinations of the skew-t -normal Birnbaum-Saunders distributions and is suitable for modelling heavy-tailed data with a heterogeneous population. These distributions are then used to estimate the wind speed distribution. The performance of the proposed family has been compared with five mixture models of the already used distributions, using wind speed data collected at nine stations across Ontario, Canada. The results indicate that mixture models generally provide a better fit than unimodal distributions, according to the model selection criterion. Based on the obtained results, the proposed family provides highly flexible models at all selected stations. It functions better than the other considered distributions at seven of the stations, whereas it is ranked second in the remaining two stations. The proposed family can be utilized in a widespread manner to describe the wind speed in Canada, as well as other regions with similar features. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Birnbaum-saunders distribution Wind speed distribution em-algorithm Heavy-tailed distribution Multimodal histogram Wind power

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Score-adjusted methods for estimation of shape parameters in Gamma-Poisson and Beta-Binomial distributions

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年第3期53卷 1247-1257页

作者： Tamae, Hiromasa Irie, Kaoru Kubokawa, Tatsuya Univ Tokyo Grad Sch Econ Tokyo Japan Univ Tokyo Fac Econ 7-3-1 Hongo Tokyo 1130033 Japan

The gamma-Poisson and beta-binomial mixture distributions are used for analyzing count-valued data, and the estimation of the hyper-parameters including the shape and/or scale parameters is important in the empirical Bayes inference. The maximum likelihood method requires the nested loops for solving the non-linear equations at each step of iteration in the em algorithm. To avoid the extra loops, we derive the closed-form updating procedures at each step of iteration by using the score-adjusted method. The performance is compared by simulation with the maximum likelihood estimators.

关键词： Beta-binomial distribution em-algorithm Gamma-Poisson distribution Maximum likelihood estimate Moment method Score function

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Statistical Consistency for Change Point Detection and Community Estimation in Time-Evolving Dynamic Networks

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2022年 8卷 215-227页

作者： Xu, Cong Lee, Thomas C. M. Univ Calif Davis Dept Stat Davis CA 95616 USA

Suppose a time sequence of networks is observed. It is known that the probabilistic behaviors of the networks do not change over time, except at a few time points. These time points are usually called change points, whose number and locations are unknown. This paper proposes a method for automatically estimating such change points and the community structures of the networks. The proposed method invokes the minimum description length principle to derive a model selection criterion, where the best estimates are defined as its minimizer. It is shown that this selection criterion yields consistent estimates for the change points as well as the community structures. For practical minimization of the selection criterion, a bottom-up search algorithm that combines the em-algorithm with variational approximation is developed. The promising empirical properties of the proposed method are illustrated via a sequence of numerical experiments and applications to some real datasets. To the best of the authors' knowledge, this method is one of the earliest that provides consistent estimates in the context of change point detection for time-evolving networks.

关键词： Stochastic processes Codes Data models Information processing Task analysis Social networking (online) Search problems em-algorithm minimum description length principle stochastic block model time series of networks variational approximation

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Additive regularization of topic models

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MACHINE LEARNING 2015年第1-3期101卷 303-323页

作者： Vorontsov, Konstantin Potapenko, Anna RAS Inst Phys & Technol Dept Intelligent Syst Dorodnicyn Comp Ctr Moscow 117901 Russia Higher Sch Econ Dept Comp Sci Moscow Russia

Probabilistic topic modeling of text collections has been recently developed mainly within the framework of graphical models and Bayesian inference. In this paper we introduce an alternative semi-probabilistic approach, which we call additive regularization of topic models (ARTM). Instead of building a purely probabilistic generative model of text we regularize an ill-posed problem of stochastic matrix factorization by maximizing a weighted sum of the log-likelihood and additional criteria. This approach enables us to combine probabilistic assumptions with linguistic and problem-specific requirements in a single multi-objective topic model. In the theoretical part of the work we derive the regularized em-algorithm and provide a pool of regularizers, which can be applied together in any combination. We show that many models previously developed within Bayesian framework can be inferred easier within ARTM and in some cases generalized. In the experimental part we show that a combination of sparsing, smoothing, and decorrelation improves several quality measures at once with almost no loss of the likelihood.

关键词： Probabilistic topic modeling Regularization of ill-posed problems Probabilistic latent sematic analysis Latent Dirichlet allocation em-algorithm

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Exponentiated Weibull-Poisson distribution: Model, properties and applications

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MATHemATICS AND COMPUTERS IN SIMULATION 2013年 92卷 76-97页

作者： Mahmoudi, Eisa Sepahdar, Afsaneh Yazd Univ Dept Stat Yazd Iran

In this paper we propose a new four-parameters distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate, called as the exponentiated Weibull-Poisson (EWP) distribution. The new distribution arises on a latent complementary risk problem base and is obtained by compounding exponentiated Weibull (EW) and Poisson distributions. This distribution contains several lifetime sub-models such as: generalized exponential-Poisson (GEP), complementary Weibull-Poisson (CWP), complementary exponential-Poisson (CEP), exponentiated Rayleigh-Poisson (ERP) and Rayleigh-Poisson (RP) distributions. We obtain several properties of the new distribution such as its probability density function, its reliability and failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via an em-algorithm is presented in this paper. Sub-models of the EWP distribution are studied in details. In the end, applications to two real data sets are given to show the flexibility and potentiality of the new distribution. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： em-algorithm Exponentiated Weibull distribution Maximum likelihood estimation Probability weighted moments Residual life function

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A Thresholding algorithm for Order Selection in Finite Mixture Models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2015年第2期44卷 433-453页

作者： Xu, Chen Chen, Jiahua Univ British Columbia Dept Stat Vancouver BC V6T 1Z4 Canada

Order selection is an important step in the application of finite mixture models. Classical methods such as AIC and BIC discourage complex models with a penalty directly proportional to the number of mixing components. In contrast, Chen and Khalili propose to link the penalty to two types of overfitting. In particular, they introduce a regularization penalty to merge similar subpopulations in a mixture model, where the shrinkage idea of regularized regression is seamlessly employed. However, the new method requires an effective and efficient algorithm. When the popular expectation-maximization (em)algorithm is used, we need to maximize a nonsmooth and nonconcave objective function in the M-step, which is computationally challenging. In this article, we show that such an objective function can be transformed into a sum of univariate auxiliary functions. We then design an iterative thresholding descent algorithm (ITD) to efficiently solve the associated optimization problem. Unlike many existing numerical approaches, the new algorithm leads to sparse solutions and thereby avoids undesirable ad hoc steps. We establish the convergence of the ITD and further assess its empirical performance using both simulations and real data examples.

关键词： em-algorithm Finite mixture model Nonconvex penalties Regularization Sparsity Thresholding

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Comparative calibration with subgroups

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2001年第10期30卷 2057-2078页

作者： Garcia-Alfaro, KH Bolfarine, H Univ Sao Paulo Dept Estat IME BR-05315970 Sao Paulo Brazil

The main object of this paper is to consider structural comparative calibration models under the assumption that the unknown quantity being measured is not identically distributed for all units. We consider the situation where the mean of the unknown quantity being measured is different within subgroups of the population. Method of moments and maximum likelihood estimators are considered for estimating the parameters in the model. Large sample inference is facilitated by the derivation of the asymptotic variances. An application to a data set which indeed motivated the consideration of such general model and was obtained by measuring the heights of a group of trees with five different instruments is considered.

关键词： asymptotic covariance matrix em-algorithm instruments precision moment estimators structural model tree heights Wald statistics

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The generalized modified Weibull power series distribution: Theory and applications

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2016年 94卷 136-160页

作者： Bagheri, S. F. Samani, E. Bahrami Ganjali, M. Shahid Beheshti Univ Dept Stat Tehran Iran

A new distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate forms called as the generalized modified Weibull power series (GMWPS) distribution is proposed. The new distribution is constructed based on a latent complementary risk problem and is obtained by compounding generalized modified Weibull (GMW) and power series distributions. The new distribution contains, as special submodels, several important distributions which are discussed in the literature, such as generalized modified Weibull Poisson (GMWP) distribution, generalized modified Weibull Geometric (GMWG) distribution, generalized modified Weibull Logarithmic (GMWL) distribution, generalized modified Weibull Binomial (GMWB) distribution, among others. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival function, failure rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Renyi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formula for the elements of the Fisher information matrix. We consider the em-algorithm for computing the estimates. Simulation studies and two real data set applications are also given for illustration of the flexibility and potentiality of the new distribution. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Generalized modified Weibull distribution Power series distributions Goodness-of-fit tests Hazard function em-algorithm Fisher's information matrix Residual life function

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Parameter estimation from incomplete data in binomial regression when the missing data mechanism is nonignorable

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BIOMETRICS 1996年第3期52卷 1071-1078页

作者： Ibrahim, JG Lipsitz, SR DANA FARBER CANC INST DIV BIOSTATBOSTONMA 02115

We propose a method for estimating parameters in binomial regression models when the response variable is missing and the missing data mechanism is nonignorable. We assume throughout that the covariates are fully observed. Using a legit model for the missing data mechanism, we show how parameter estimation can be accomplished using the em algorithm by the method of weights proposed in Ibrahim (1990, Journal of the American Statistical Association 85, 765-769). An example from the Six Cities Study (Ware et al., 1984, American Review of Respiratory Diseases 129, 366-374) is presented to illustrate the method.

关键词： em-algorithm generalized linear models nonignorable missing data

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