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One-shot device test data analysis using non-parametric and semi-parametric inferential methods and applications

RELIABILITY ENGINEERING & SYSTEM SAFETY 2022年 221卷

作者： Zhu, Xiaojun Balakrishnan, N. Xian Jiaotong Liverpool Univ Dept Financial & Actuarial Math Suzhou 215123 Peoples R China McMaster Univ Dept Math & Stat Hamilton ON L8S 4K1 Canada

A one-shot device, such as an automobile airbag, electro-explosive unit or munition, is a product that can be used only once. Its actual lifetime is unobservable, rendering the corresponding reliability analysis quite challenging. In this paper, two non-parametric methodologies-maximum likelihood estimation via EM-algorithm and Nelson-Aalen based estimation are developed for identical testing environment on one-shot devices. The EM-algorithm is usually used for unobserved failure times under some specific parametric models. But, here the EM-algorithm is adopted for the number of failures in each time interval in a nonparametric manner. Next, a semi-parametric approach, based on proportional hazards assumption, is developed for nonidentical testing environments, such as under an accelerated life-test. A Monte Carlo simulation study is then carried out for evaluating the performance of the inferential methods developed here. Finally, two data sets are analyzed for illustrative purpose.

关键词： Accelerated life-test expectation-maximization algorithm Kaplan-Meier estimator Nelson-Aalen estimator Non-parametric inference One-shot device test Proportional hazards model Semi-parametric inference

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Moments of Mixture Periodic Autoregressive Models

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2011年第22期40卷 3937-3947页

作者： Bentarzi, M. Merzougui, M. Univ Sci & Technol USTHB Algiers Algeria Univ MHamed Bouguera Boumerdes Algeria

This article deals with the study of some properties of a mixture periodically correlated autoregressive (MPAR(S)) time series model, which extends the mixture time invariant parameter autoregressive (MAR) model, that has recently received a considerable interest from many economic time series analysts, to mixture periodic parameter autoregressive model. The aim behind this extension is to make the model able to capture, in addition to all features captured by the classical MAR model, the periodicity feature exhibited by the autocovariance structure of many encountered financial and environmental time series with eventual multimodal distributions. Our main contribution here is obtaining of the second moment periodically stationary condition for a MPAR(S) (K;2, ... , 2) model, furthermore the closed-form of the second moment is obtained.

关键词： expectation-maximization algorithm Mixture periodic autoregressive models Periodic autoregressive models Periodically correlated process

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An EM algorithm-Based Disintegrated Channel Estimator for OFDM AF Cooperative Relaying

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IEICE TRANSACTIONS ON COMMUNICATIONS 2013年第1期E96B卷 254-262页

作者： Sheu, Jeng-Shin Sheen, Wern-Ho Natl Yunlin Univ Sci & Technol Dept Comp Sci & Informat Engn Touliu Yunlin Taiwan Chaoyang Univ Technol Dept Informat & Commun Engn Taichung Taiwan

The cooperative orthogonal frequency-division multiplexing (OFDM) relaying system is widely regarded as a key design for future broadband mobile cellular systems. This paper focuses on channel estimation in such a system that uses amplify-and-forward (AF) as the relaying strategy. In the cooperative AF relaying, the destination requires the individual (disintegrated) channel state information (CSI) of the source-relay (S-R) and relay-destination (R-D) links for optimum combination of the signals received from source and relay. Traditionally, the disintegrated CSIs are obtained with two channel estimators: one at the relay and the other at the destination. That is, the CSI of the S-R link is estimated at relay and passed to destination, and the CSI of the R-D link is estimated at destination with the help of pilot symbols transmitted by relay. In this paper, a new disintegrated channel estimator is proposed;based on an expectation-maximization (EM) algorithm, the disintegrated CSIs can be estimated solely by the estimator at destination. Therefore, the new method requires neither signaling overhead for passing the CSI of the S-R link to destination nor pilot symbols for the estimation of the R-D link. Computer simulations show that the proposed estimator works well under the signal-to-noise ratios of interest.

关键词： channel estimation orthogonal frequency-division multiplexing amplify-and-forward relaying expectation-maximization algorithm

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MODELING AND CLASSIFICATION OF DEATHS DUE TO COVID-19 BASED ON MACHINE LEARNING TECHNIQUE

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THERMAL SCIENCE 2023年第1期27卷 405-410页

作者： Alharbi, Randa Univ Tabuk Fac Sci Dept Stat Tabuk Saudi Arabia

Statistical classification is recently considered one of the most important and most common methods in machine learning models and consists of building mod-els that define the target of research interest. There are many classification methods that can be used to predict the value of a response. In this article, we are interested in machine learning applications to classify the new deaths due to Covid-19. Under consideration BIC criterion, the experimental results have shown that the E (Equal variance) with four is the best mixture model. The con-vergence in the algorithm of expectation-maximization is satisfied after 167 itera-tions. The World Health Organization has presented the source of data over the period of March 2, 2020 to August 5, 2020.

关键词： expectation-maximization algorithm machine learning modeling classification Gaussian mixtures model prediction

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Trajectory Modeling of Longitudinal Binary Data: Application of the EM algorithm for Mixture Models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2014年第3期43卷 495-519页

作者： Chu, Man-Kee M. Koval, John J. Univ Western Ontario Dept Stat & Actuarial Sci London ON N6A 5B7 Canada Univ Western Ontario Dept Epidemiol & Biostat London ON N6A 5B7 Canada

A developmental trajectory describes the course of behavior over time. Identifying multiple trajectories within an overall developmental process permits a focus on subgroups of particular interest. We introduce a framework for identifying trajectories by using the expectation-maximization (EM) algorithm to fit semiparametric mixtures of logistic distributions to longitudinal binary data. For performance comparison, we consider full maximization algorithms (PROC TRAJ in SAS), standard EM, and two other EM-based algorithms for speeding up convergence. Simulation shows that EM methods produce more accurate parameter estimates. The EM methodology is illustrated with a longitudinal dataset involving adolescents smoking behaviors.

关键词： Binary data expectation-maximization algorithm Longitudinal trajectories Mixture models

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Inference for an Inverted Exponentiated Pareto Distribution Under Progressive Censoring

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2019年第1期13卷 1-32页

作者： Maurya, Raj Kamal Tripathi, Yogesh Mani Sen, Tanmay Rastogi, Manoj Kumar Indian Inst Technol Patna Dept Math Bihta 801106 India Patna Univ Dept Stat Patna 800005 Bihar India

In this paper, estimation of unknown parameters of an inverted exponentiated Pareto distribution is considered under progressive Type-II censoring. Maximum likelihood estimates are obtained from the expectation-maximization algorithm. We also compute the observed Fisher information matrix. In the sequel, asymptotic and bootstrap-p intervals are constructed. Bayes estimates are derived using the importance sampling procedure with respect to symmetric and asymmetric loss functions. Highest posterior density intervals of unknown parameters are constructed as well. The problem of one- and two-sample prediction is discussed in Bayesian framework. Optimal plans are obtained with respect to two information measure criteria. We assess the behavior of suggested estimation and prediction methods using a simulation study. A real dataset is also analyzed for illustration purposes. Finally, we present some concluding remarks.

关键词： expectation-maximization algorithm Bootstrap interval Importance sampling method HPD interval Bayes prediction Optimal censoring

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A Study of EM algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

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Open Journal of Modelling and Simulation 2024年第2期12卷 33-42页

作者： Yisa Adeniyi Abolade Yichuan Zhao Department of Mathematics and Statistics Georgia State University Atlanta Georgia USA

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

关键词： Compositional Data Linear Regression Model Least Square Method Robust Least Square Method Synthetic Data Aitchison Distance Maximum Likelihood Estimation expectation-maximization algorithm k-Nearest Neighbor and Mean imputation

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Discrete Latent Variable Models

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Statistics and Its Application 1000年第1期9卷 425-452页

作者： Francesco Bartolucci Silvia Pandolfi Fulvia Pennoni 1Department of Economics University of Perugia Perugia 06123 Italy email: francesco.bartolucci@unipg.itsilvia.pandolfi@unipg.it 2Department of Statistics and Quantitative Methods University of Milano-Bicocca Milan 20126 Italy email: fulvia.pennoni@unimib.it

We review the discrete latent variable approach, which is very popular in statistics and related fields. It allows us to formulate interpretable and flexible models that can be used to analyze complex datasets in the presence of articulated dependence structures among variables. Specific models including discrete latent variables are illustrated, such as finite mixture, latent class, hidden Markov, and stochastic block models. algorithms for maximum likelihood and Bayesian estimation of these models are reviewed, focusing, in particular, on the expectation–maximization algorithm and the Markov chain Monte Carlo method with data augmentation. Model selection, particularly concerning the number of support points of the latent distribution, is discussed. The approach is illustrated by summarizing applications available in the literature; a brief review of the main software packages to handle discrete latent variable models is also provided. Finally, some possible developments in this literature are suggested.

关键词： data augmentation expectation-maximization algorithm finite mixture model hidden Markov model latent class model model selection stochastic block model

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Direct Importance Estimation with a Mixture of Probabilistic Principal Component Analyzers

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2010年第10期E93D卷 2846-2849页

作者： Yamada, Makoto Sugiyama, Masashi Wichern, Gordon Simm, Jaak Tokyo Inst Technol Tokyo 1528552 Japan JST PRESTO Tokyo 1528552 Japan MIT Lincoln Lab Lexington MA 02420 USA

Estimating the ratio of two probability density functions (a.k.a. the importance) has recently gathered a great deal of attention since importance estimators can be used for solving various machine learning and data mining problems. In this paper, we propose a new importance estimation method using a mixture of probabilistic principal component analyzers. The proposed method is more flexible than existing approaches, and is expected to work well when the target importance function is correlated and rank-deficient. Through experiments, we illustrate the validity of the proposed approach.

关键词： importance Kullback-Leibler importance estimation procedure mixture of probabilistic principal component analyzers expectation-maximization algorithm

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Model Parameter Estimation and Residual Life Prediction for a Partially Observable Failing System

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NAVAL RESEARCH LOGISTICS 2015年第3期62卷 190-205页

作者： Khaleghei, Akram Makis, Viliam Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

We consider a partially observable degrading system subject to condition monitoring and random failure. The system's condition is categorized into one of three states: a healthy state, a warning state, and a failure state. Only the failure state is observable. While the system is operational, vector data that is stochastically related to the system state is obtained through condition monitoring at regular sampling epochs. The state process evolution follows a hidden semi-Markov model (HSMM) and Erlang distribution is used for modeling the system's sojourn time in each of its operational states. The expectation-maximization (EM) algorithm is applied to estimate the state and observation parameters of the HSMM. Explicit formulas for several important quantities for the system residual life estimation such as the conditional reliability function and the mean residual life are derived in terms of the posterior probability that the system is in the warning state. Numerical examples are presented to demonstrate the applicability of the estimation procedure and failure prediction method. A comparison results with hidden Markov modeling are provided to illustrate the effectiveness of the proposed model. (c) 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 190-205, 2015

关键词： condition-based maintenance reliability mean residual life hidden semi-Markov model expectation-maximization algorithm

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