Robust Mixture Regression Models Using T Distribution

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Robust Mixture Regression Models Using T-distribution

Author : Yan Wei
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (86 download)

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Book Synopsis Robust Mixture Regression Models Using T-distribution by : Yan Wei

Download or read book Robust Mixture Regression Models Using T-distribution written by Yan Wei and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report, we propose a robust mixture of regression based on t-distribution by extending the mixture of t-distributions proposed by Peel and McLachlan (2000) to the regression setting. This new mixture of regression model is robust to outliers in y direction but not robust to the outliers with high leverage points. In order to combat this, we also propose a modified version of the proposed method, which fits the mixture of regression based on t-distribution to the data after adaptively trimming the high leverage points. We further propose to adaptively choose the degree of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degree of freedom. We demonstrate the effectiveness of the proposed new method and compare it with some of the existing methods through simulation study.

Robust Mixtures of Regression Models

Author : Xiuqin Bai
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (899 download)

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Book Synopsis Robust Mixtures of Regression Models by : Xiuqin Bai

Download or read book Robust Mixtures of Regression Models written by Xiuqin Bai and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t-distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails.

Robust Mixture Linear EIV Regression Models by T-distribution

Author : Yantong Liu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (823 download)

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Book Synopsis Robust Mixture Linear EIV Regression Models by T-distribution by : Yantong Liu

Download or read book Robust Mixture Linear EIV Regression Models by T-distribution written by Yantong Liu and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A robust estimation procedure for mixture errors-in-variables linear regression models is proposed in the report by assuming the error terms follow a t-distribution. The estimation procedure is implemented by an EM algorithm based on the fact that the t-distribution is a scale mixture of normal distribution and a Gamma distribution. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies. Comparison is also made with the MLE procedure under normality assumption.

Österreichisches UNIX Forum ; 5

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (258 download)

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Book Synopsis Österreichisches UNIX Forum ; 5 by :

Download or read book Österreichisches UNIX Forum ; 5 written by and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mixture Models

Author : Weixin Yao
Publisher : CRC Press
ISBN 13 : 1040009875
Total Pages : 398 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Mixture Models by : Weixin Yao

Download or read book Mixture Models written by Weixin Yao and published by CRC Press. This book was released on 2024-04-18 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixture models are a powerful tool for analyzing complex and heterogeneous datasets across many scientific fields, from finance to genomics. Mixture Models: Parametric, Semiparametric, and New Directions provides an up-to-date introduction to these models, their recent developments, and their implementation using R. It fills a gap in the literature by covering not only the basics of finite mixture models, but also recent developments such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling. Features Comprehensive overview of the methods and applications of mixture models Key topics include hypothesis testing, model selection, estimation methods, and Bayesian approaches Recent developments, such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling Examples and case studies from such fields as astronomy, biology, genomics, economics, finance, medicine, engineering, and sociology Integrated R code for many of the models, with code and data available in the R Package MixSemiRob Mixture Models: Parametric, Semiparametric, and New Directions is a valuable resource for researchers and postgraduate students from statistics, biostatistics, and other fields. It could be used as a textbook for a course on model-based clustering methods, and as a supplementary text for courses on data mining, semiparametric modeling, and high-dimensional data analysis.

Recent Advances in Robust Statistics: Theory and Applications

Author : Claudio Agostinelli
Publisher : Springer
ISBN 13 : 8132236432
Total Pages : 204 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Recent Advances in Robust Statistics: Theory and Applications by : Claudio Agostinelli

Download or read book Recent Advances in Robust Statistics: Theory and Applications written by Claudio Agostinelli and published by Springer. This book was released on 2016-11-10 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a collection of recent contributions and emerging ideas in the areas of robust statistics presented at the International Conference on Robust Statistics 2015 (ICORS 2015) held in Kolkata during 12–16 January, 2015. The book explores the applicability of robust methods in other non-traditional areas which includes the use of new techniques such as skew and mixture of skew distributions, scaled Bregman divergences, and multilevel functional data methods; application areas being circular data models and prediction of mortality and life expectancy. The contributions are of both theoretical as well as applied in nature. Robust statistics is a relatively young branch of statistical sciences that is rapidly emerging as the bedrock of statistical analysis in the 21st century due to its flexible nature and wide scope. Robust statistics supports the application of parametric and other inference techniques over a broader domain than the strictly interpreted model scenarios employed in classical statistical methods. The aim of the ICORS conference, which is being organized annually since 2001, is to bring together researchers interested in robust statistics, data analysis and related areas. The conference is meant for theoretical and applied statisticians, data analysts from other fields, leading experts, junior researchers and graduate students. The ICORS meetings offer a forum for discussing recent advances and emerging ideas in statistics with a focus on robustness, and encourage informal contacts and discussions among all the participants. They also play an important role in maintaining a cohesive group of international researchers interested in robust statistics and related topics, whose interactions transcend the meetings and endure year round.

Robust Multivariate Mixture Regression Models

Author : Xiongya Li
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (14 download)

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Book Synopsis Robust Multivariate Mixture Regression Models by : Xiongya Li

Download or read book Robust Multivariate Mixture Regression Models written by Xiongya Li and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we proposed a new robust estimation procedure for two multivariate mixture regression models and applied this novel method to functional mapping of dynamic traits. In the first part, a robust estimation procedure for the mixture of classical multivariate linear regression models is discussed by assuming that the error terms follow a multivariate Laplace distribution. An EM algorithm is developed based on the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution. The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies. In the second part, the similar idea is extended to the mixture of linear mixed regression models by assuming that the random effect and the regression error jointly follow a multivariate Laplace distribution. Compared with the existing robust t procedure in the literature, simulation studies indicate that the finite sample performance of the proposed estimation procedure outperforms or is at least comparable to the robust t procedure. Comparing to t procedure, there is no need to determine the degrees of freedom, so the new robust estimation procedure is computationally more efficient than the robust t procedure. The ascent property for both EM algorithms are also proved. In the third part, the proposed robust method is applied to identify quantitative trait loci (QTL) underlying a functional mapping framework with dynamic traits of agricultural or biomedical interest. A robust multivariate Laplace mapping framework was proposed to replace the normality assumption. Simulation studies show the proposed method is comparable to the robust multivariate t-distribution developed in literature and outperforms the normal procedure. As an illustration, the proposed method is also applied to a real data set.

Robust Mixture Regression Modeling with Pearson Type VII Distribution

Author : Jingyi Zhang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (851 download)

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Book Synopsis Robust Mixture Regression Modeling with Pearson Type VII Distribution by : Jingyi Zhang

Download or read book Robust Mixture Regression Modeling with Pearson Type VII Distribution written by Jingyi Zhang and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A robust estimation procedure for parametric regression models is proposed in the paper by assuming the error terms follow a Pearson type VII distribution. The estimation procedure is implemented by an EM algorithm based on the fact that the Pearson type VII distributions are a scale mixture of a normal distribution and a Gamma distribution. A trimmed version of proposed procedure is also discussed in this paper, which can successfully trim the high leverage points away from the data. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in the literature.

Finite Mixture Models

Author : Geoffrey McLachlan
Publisher : John Wiley & Sons
ISBN 13 : 047165406X
Total Pages : 419 pages
Book Rating : 4.4/5 (716 download)

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Book Synopsis Finite Mixture Models by : Geoffrey McLachlan

Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.

Statistical Analysis of Finite Mixture Distributions

Author : D. M. Titterington
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Statistical Analysis of Finite Mixture Distributions by : D. M. Titterington

Download or read book Statistical Analysis of Finite Mixture Distributions written by D. M. Titterington and published by . This book was released on 1985 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors give a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions.

An Introduction to Regression Graphics

Author : R. Dennis Cook
Publisher : John Wiley & Sons
ISBN 13 : 0470317701
Total Pages : 282 pages
Book Rating : 4.4/5 (73 download)

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Book Synopsis An Introduction to Regression Graphics by : R. Dennis Cook

Download or read book An Introduction to Regression Graphics written by R. Dennis Cook and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the use of dynamic and interactive computer graphics in linear regression analysis, focusing on analytical graphics. Features new techniques like plot rotation. The authors have composed their own regression code, using Xlisp-Stat language called R-code, which is a nearly complete system for linear regression analysis and can be utilized as the main computer program in a linear regression course. The accompanying disks, for both Macintosh and Windows computers, contain the R-code and Xlisp-Stat. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Robust Mixture Regression Model Fitting by Laplace Distribution

Author : Yanru Xing
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (859 download)

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Book Synopsis Robust Mixture Regression Model Fitting by Laplace Distribution by : Yanru Xing

Download or read book Robust Mixture Regression Model Fitting by Laplace Distribution written by Yanru Xing and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A robust estimation procedure for mixture linear regression models is proposed in this report by assuming the error terms follow a Laplace distribution. EM algorithm is imple- mented to conduct the estimation procedure of missing information based on the fact that the Laplace distribution is a scale mixture of normal and a latent distribution. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in this literature. A sensitivity study is also conducted based on a real data example to illustrate the application of the proposed method.

Finite Mixture of Skewed Distributions

Author : Víctor Hugo Lachos Dávila
Publisher : Springer
ISBN 13 : 3319980297
Total Pages : 108 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Finite Mixture of Skewed Distributions by : Víctor Hugo Lachos Dávila

Download or read book Finite Mixture of Skewed Distributions written by Víctor Hugo Lachos Dávila and published by Springer. This book was released on 2018-11-12 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book. This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry.

Finite Mixture and Markov Switching Models

Author : Sylvia Frühwirth-Schnatter
Publisher : Springer Science & Business Media
ISBN 13 : 0387357688
Total Pages : 506 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Finite Mixture and Markov Switching Models by : Sylvia Frühwirth-Schnatter

Download or read book Finite Mixture and Markov Switching Models written by Sylvia Frühwirth-Schnatter and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.

Applied Regression Analysis

Author : Norman R. Draper
Publisher : John Wiley & Sons
ISBN 13 : 0471170828
Total Pages : 736 pages
Book Rating : 4.4/5 (711 download)

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Book Synopsis Applied Regression Analysis by : Norman R. Draper

Download or read book Applied Regression Analysis written by Norman R. Draper and published by John Wiley & Sons. This book was released on 1998-04-23 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ein Hauptziel wissenschaftlicher Forschung ist das Auffinden von Beziehungen zwischen Variablen. Die Regressionsrechnung ist ein allgemein gebräuchliches statistisches Mittel zur Erstellung von mathematischen Modellen aus Forschungsdaten. Die 3. Auflage wurde um 16 neue Kapitel erweitert; die Grundlagen der Regressionsrechnung werden, ausgehend von klassischen Konzepten, präzise erklärt. Mit vielen Übungsaufgaben und Lösungen sowie einer Diskette. (06/98)

Finite Mixture Distributions

Author : B. Everitt
Publisher : Springer Science & Business Media
ISBN 13 : 9400958978
Total Pages : 148 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Finite Mixture Distributions by : B. Everitt

Download or read book Finite Mixture Distributions written by B. Everitt and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. The literature surrounding them is large and goes back to the end of the last century when Karl Pearson published his well-known paper on estimating the five parameters in a mixture of two normal distributions. In this text we attempt to review this literature and in addition indicate the practical details of fitting such distributions to sample data. Our hope is that the monograph will be useful to statisticians interested in mixture distributions and to re search workers in other areas applying such distributions to their data. We would like to express our gratitude to Mrs Bertha Lakey for typing the manuscript. Institute oj Psychiatry B. S. Everitt University of London D. l Hand 1980 CHAPTER I General introduction 1. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions. Such superpositions are termed mixture distributions or compound distributions. For example, the distribution of height in a population of children might be expressed as follows: h(height) = fg(height: age)f(age)d age (1. 1) where g(height: age) is the conditional distribution of height on age, and/(age) is the age distribution of the children in the population.

Nonparametric Statistics and Mixture Models

Author : David R. Hunter
Publisher : World Scientific
ISBN 13 : 9814340553
Total Pages : 370 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Nonparametric Statistics and Mixture Models by : David R. Hunter

Download or read book Nonparametric Statistics and Mixture Models written by David R. Hunter and published by World Scientific. This book was released on 2011 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This festschrift includes papers authored by many collaborators, colleagues, and students of Professor Thomas P Hettmansperger, who worked in research in nonparametric statistics, rank statistics, robustness, and mixture models during a career that spanned nearly 40 years. It is a broad sample of peer-reviewed, cutting-edge research related to nonparametrics and mixture models.