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Autoregressive processes with generalized hyperbolic innovations

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2020年第12期49卷 3080-3092页

作者： Ghasami, Safdar Khodadadi, Zahra Maleki, Mohsen Islamic Azad Univ Marvdasht Branch Dept Stat Marvdasht Iran Shiraz Univ Dept Stat Shiraz Iran

This article investigates autoregressive processes with the flexible and attractive symmetric/asymmetric and light/heavy tailed Generalized-Hyperbolic innovations. The Generalized-Hyperbolic family of distributions has an interesting stochastic representation which can be used in simulating the proposed autoregressive model and estimating its parameters via an Expectation-Maximization (em) type algorithm. The performance of the proposed model and its estimation through a simulation study is also evaluated. The model is then applied on two real-time series datasets.

关键词： Autoregressive model em-algorithm Generalized-hyperbolic Generalized inverse Gaussian Hierarchical representation

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Statistical inference for coherent systems with Weibull distributed component lifetimes under complete and incomplete information

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2019年第4期35卷 1011-1027页

作者： Jablonka, A. Cramer, E. Hermanns, M. Rhein Westfal TH Aachen Inst Stat D-52056 Aachen Germany

Point estimators for the parameters of the component lifetime distribution in coherent systems are evolved assuming to be independently and identically Weibull distributed component lifetimes. We study both complete and incomplete information under continuous monitoring of the essential component lifetimes. First, we prove that the maximum likelihood estimator (MLE) under complete information based on progressively Type-II censored system lifetimes uniquely exists and we present two approaches to compute the estimates. Furthermore, we consider an ad hoc estimator, a max-probability plan estimator and the MLE for the parameters under incomplete information. In order to compute the MLEs, we consider a direct maximization of the likelihood and an em-algorithm-type approach, respectively. In all cases, we illustrate the results by simulations of the five-component bridge system and the 10-component parallel system, respectively.

关键词： bridge system coherent system em-algorithm likelihood inference progressive Type-II censoring signature Weibull distribution

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Regression modeling of ordinal data with nonzero baselines

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BIOMETRICS 1999年第1期55卷 308-316页

作者： Xie, MG Simpson, DG Natl Inst Stat Sci Res Triangle Pk NC 27709 USA

This paper develops regression models for ordinal data with nonzero control response probabilities. The models are especially useful in dose-response studies where the spontaneous or natural response rate is nonnegligible and the dosage is logarithmic. These models generalize Abbott's formula, which has been commonly used to model binary data with nonzero background observations. We describe a biologically plausible latent structure and develop an em algorithm for fitting the models. The em algorithm can be implemented using standard software for ordinal regression. A toxicology data set where the proposed model fits the data but a more conventional model fails is used to illustrate the methodology.

关键词： em-algorithm latent structure nonzero baseline model ordinal data risk assessment

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Joint discrete and continuous matrix distribution modeling

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STOCHASTIC MODELS 2024年第1期40卷 1-37页

作者： Bladt, Martin Gardner, Clara Brimnes Univ Copenhagen Dept Math Sci Copenhagen Denmark Tech Univ Denmark DTU Compute Lyngby Denmark Tech Univ Denmark DTU Compute DK-2800 Lyngby Denmark

In this paper, we introduce a bivariate distribution on R(+)xN arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on R(+)xN and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective em algorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models.

关键词： Markov processes phase-type distributions mixed data em-algorithm

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Hidden markov models in reliability and maintenance

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第3期304卷 1242-1255页

作者： Gamiz, Maria Luz Limnios, Nikolaos Segovia-Garcia, Maria Del Carmen Univ Granada Granada Spain Univ Technol Compiegne Compiegne France

Although the hidden Markov models (HMM) are very popular in many applied areas their use in reliabil-ity engineering is limited. Problems such as the selection of the HMM model by choosing the appropriate number of states, or problems of prediction of failures have not been widely covered in the literature. This paper is concerned with the use of HMMs where the state of the system is not directly observable and instead certain indicators of the true situation are provided via a control system. A hidden model can provide key information about the system dependability such as the failed component of the sys-tem, the reliability of the system and related measures. A maximum-likelihood estimator of the system reliability is obtained and its asymptotic properties are studied. Finally, the maintenance of the system is considered in this context and new preventive maintenance strategies are defined and their efficiency is measured in terms of expected cost. To prove the finite sample performance of the methodology, an extensive simulation study is developed.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Reliability Hidden Markov chain Maintenance Asymptotic properties em-algorithm

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An Alternative Estimation Approach for the Heterogeneity Linear Mixed Model

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2014年第10期43卷 2628-2638页

作者： Martinez, Marie-Jose Holian, emma INRIA Grenoble Rhone Alpes Team MISTIS F-38334 Saint Ismier France Lab Jean Kuntzmann F-38334 Saint Ismier France Natl Univ Ireland Sch Math Dept Stat & Appl Math Galway Ireland

In this article, an alternative estimation approach is proposed to fit linear mixed effects models where the random effects follow a finite mixture of normal distributions. This heterogeneity linear mixed model is an interesting tool since it relaxes the classical normality assumption and is also perfectly suitable for classification purposes, based on longitudinal profiles. Instead of fitting directly the heterogeneity linear mixed model, we propose to fit an equivalent mixture of linear mixed models under some restrictions which is computationally simpler. Unlike the former model, the latter can be maximized analytically using an em-algorithm and the obtained parameter estimates can be easily used to compute the parameter estimates of interest.

关键词： Heterogeneous model em-algorithm Linear mixed model Mixture model Repeated measurements

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Model-based clustering for multivariate functional data

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2014年 71卷 92-106页

作者： Jacques, Julien Preda, Cristian Univ Lille 1 Lab Paul Painleve UMR CNRS 8524 Lille France INRIA Lille Nord Europe MODAL Team Lille France Polytech Lille Lille France

The first model-based clustering algorithm for multivariate functional data is proposed. After introducing multivariate functional principal components analysis (MFPCA), a parametric mixture model, based on the assumption of normality of the principal component scores, is defined and estimated by an em-like algorithm. The main advantage of the proposed model is its ability to take into account the dependence among curves. Results on simulated and real datasets show the efficiency of the proposed method. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Multivariate functional data Density approximation Model-based clustering Multivariate functional principal component analysis em-algorithm

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Penalized maximum likelihood estimator for finite multivariate skew normal mixtures

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第23期52卷 8280-8305页

作者： Wu, Weisan Li, Shaoting Baicheng Normal Univ Sch Math & Stat Baicheng Peoples R China Dongbei Univ Finance & Econ Sch Stat 217 Jianshan St Dalian 116025 Peoples R China

In practice, multivariate skew normal mixture (MSNM) models provide a more flexible framework than multivariate normal mixture models, especially for heterogeneous and asymmetric data. For MSNM models, the maximum likelihood estimator often leads to a statistical inference referred to as "badness" under certain properties, because of the unboundedness of the likelihood function and the divergence of shape parameters. We consider two penalties for the log-likelihood function to counter these issues simultaneously in MSNM models. We show that the penalized maximum likelihood estimator is strongly consistent when the putative order of the mixture is equal to or larger than the true order. We also provide penalized expectation-maximization-type algorithms to compute penalized estimates. Finite sample performance is examined through simulations, real data applications, and comparison with existing methods.

关键词： Consistency em-algorithm finite mixture penalized likelihood skewness

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Reliability of one-shot device with generalized gamma lifetime under cyclic accelerated life-test

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY 2022年第6期236卷 1007-1023页

作者： Zhu, Xiaojun Liu, Kai Xian Jiaotong Liverpool Univ Dept Math Sci Suzhou Peoples R China Shanghai Lixin Univ Accounting & Finance Sch Stat & Math Interdisciplinary Res Inst Data Sci Room 208Teaching Bldg 1995 Shangchuan Rd Shanghai 201209 Peoples R China

One-shot devices are products or equipments that can be used only once. A nature characteristic of one-shot devices is that they get destroyed immediately after their use, and therefore their actual lifetimes are never observable. The only information observed is the condition whether they worked or not at the time they are used. These days the quality of products are significantly improved, so that the information obtained under a normal test during a short time is quite limited. A typical test to induce more failures is the accelerated life-test, which is developed by increasing the stress levels under test. In this paper, we will investigate the reliability of one-shot devices with generalized gamma fatigue life under accelerated life-tests with various cyclic temperature fluctuations by assuming a Norris-Landzberg model. Generalized gamma involves many common lifetime distributions, such as gamma, Weibull, lognormal, and positive stable distributions, as special cases. Norris-Landzberg model takes not only temperature change, highest testing temperature, but also the cycling frequency into account when modeling the number of cycles-to-failure, resulting a generalized model with the well-known Coffin-Manson model and Coffin-Manson-Arrhenius model as special cases. Associated inferences are developed. The performance of the proposed model and inferential methods will be evaluated with simulation study and model discrimination. Finally, the chip-scale package solder joints data is analyzed to illustrate the considered model and inferential methods developed in this paper.

关键词： Accelerated life-test generalized gamma distribution Norris-Landzberg model em-algorithm one-shot device testing

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Discrete-time inverse linear quadratic optimal control over fnite time-horizon under noisy output measurements

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Control Theory and Technology 2021年第4期19卷 563-572页

作者： Han Zhang Yibei Li Xiaoming Hu Department of Automation Shanghai Jiao Tong UniversityShanghai 200240China Key Laboratory of System Control and Information Processing Ministry of Education of ChinaShanghai 200240China Shanghai Engineering Research Center of Intelligent Control and Management Shanghai 200240China Department of Mathematics KTH Royal Institute of Technology10044 StockholmSweden

In this paper,the problem of inverse quadratic optimal control over fnite time-horizon for discrete-time linear systems is *** goal is to recover the corresponding quadratic objective function using noisy ***,the identifability of the model structure for the inverse optimal control problem is analyzed under relative degree assumption and we show the model structure is strictly globally ***,we study the inverse optimal control problem whose initial state distribution and the observation noise distribution are unknown,yet the exact observations on the initial states are *** formulate the problem as a risk minimization problem and approximate the problem using empirical *** is further shown that the solution to the approximated problem is statistically consistent under the assumption of relative *** then study the case where the exact observations on the initial states are not available,yet the observation noises are known to be white Gaussian distributed and the distribution of the initial state is also Gaussian(with unknown mean and covariance).em-algorithm is used to estimate the parameters in the objective *** efectiveness of our results are demonstrated by numerical examples.

关键词： Inverse optimal control Linear quadratic regulator Statistical consistency em-algorithm

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