Robust Multivariate Mixture Regression Models

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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.

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 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.

The Birnbaum-Saunders Distribution

Author : Victor Leiva
Publisher : Academic Press
ISBN 13 : 0128038276
Total Pages : 156 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis The Birnbaum-Saunders Distribution by : Victor Leiva

Download or read book The Birnbaum-Saunders Distribution written by Victor Leiva and published by Academic Press. This book was released on 2015-10-26 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Birnbaum-Saunders Distribution presents the statistical theory, methodology, and applications of the Birnbaum-Saunders distribution, a very flexible distribution for modeling different types of data (mainly lifetime data). The book describes the most recent theoretical developments of this model, including properties, transformations and related distributions, lifetime analysis, and shape analysis. It discusses methods of inference based on uncensored and censored data, goodness-of-fit tests, and random number generation algorithms for the Birnbaum-Saunders distribution, also presenting existing and future applications. Introduces inference in the Birnbaum-Saunders distribution Provides a comprehensive review of the statistical theory and methodology of the Birnbaum-Distribution Discusses different applications of the Birnbaum-Saunders distribution Explains characterization and the lifetime analysis

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.

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 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.

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.

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:

Optimal Mixture Experiments

Author : B.K. Sinha
Publisher : Springer
ISBN 13 : 8132217861
Total Pages : 213 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Optimal Mixture Experiments by : B.K. Sinha

Download or read book Optimal Mixture Experiments written by B.K. Sinha and published by Springer. This book was released on 2014-05-24 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book dwells mainly on the optimality aspects of mixture designs. As mixture models are a special case of regression models, a general discussion on regression designs has been presented, which includes topics like continuous designs, de la Garza phenomenon, Loewner order domination, Equivalence theorems for different optimality criteria and standard optimality results for single variable polynomial regression and multivariate linear and quadratic regression models. This is followed by a review of the available literature on estimation of parameters in mixture models. Based on recent research findings, the volume also introduces optimal mixture designs for estimation of optimum mixing proportions in different mixture models, which include Scheffé’s quadratic model, Darroch-Waller model, log- contrast model, mixture-amount models, random coefficient models and multi-response model. Robust mixture designs and mixture designs in blocks have been also reviewed. Moreover, some applications of mixture designs in areas like agriculture, pharmaceutics and food and beverages have been presented. Familiarity with the basic concepts of design and analysis of experiments, along with the concept of optimality criteria are desirable prerequisites for a clear understanding of the book. It is likely to be helpful to both theoreticians and practitioners working in the area of mixture experiments.

Robust Multivariate Analysis

Author : David J. Olive
Publisher : Springer
ISBN 13 : 3319682539
Total Pages : 508 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Robust Multivariate Analysis by : David J. Olive

Download or read book Robust Multivariate Analysis written by David J. Olive and published by Springer. This book was released on 2017-11-28 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents methods that are robust to the assumption of a multivariate normal distribution or methods that are robust to certain types of outliers. Instead of using exact theory based on the multivariate normal distribution, the simpler and more applicable large sample theory is given. The text develops among the first practical robust regression and robust multivariate location and dispersion estimators backed by theory. The robust techniques are illustrated for methods such as principal component analysis, canonical correlation analysis, and factor analysis. A simple way to bootstrap confidence regions is also provided. Much of the research on robust multivariate analysis in this book is being published for the first time. The text is suitable for a first course in Multivariate Statistical Analysis or a first course in Robust Statistics. This graduate text is also useful for people who are familiar with the traditional multivariate topics, but want to know more about handling data sets with outliers. Many R programs and R data sets are available on the author’s website.

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.

Multivariate Pascal Mixture Regression Models for Correlated Claim Frequencies

Author : Dameng Tang
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Multivariate Pascal Mixture Regression Models for Correlated Claim Frequencies by : Dameng Tang

Download or read book Multivariate Pascal Mixture Regression Models for Correlated Claim Frequencies written by Dameng Tang and published by . This book was released on 2016 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we propose a multivariate Pascal mixture regression model as an alternative to understand the association between multivariate count response variables and their covariates. When compared to the copula approach, this proposed class of regression models is not only less complex but can account for more versatile dependence structures and still allow for an intuitive explanation. We examine some of the properties possessed by this class of regression models and show its connections to several other models. For fitting purposes, we use the expectation-maximization (EM) algorithm which we find to be more effective and efficient. A by-product of this algorithm is that it provides for more reliable estimated standard errors of the regression coefficients useful for inference. Four different simulation studies are conducted to examine the performance of the fitting algorithm and the versatility of the proposed model while its applicability is additionally demonstrated by fitting an automobile insurance claim count dataset. All results are satisfactory and show that the proposed model can be a promising candidate for multivariate count regression modeling.

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.

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.

Multivariate Generalized Linear Mixed Models Using R

Author : Damon Mark Berridge
Publisher : CRC Press
ISBN 13 : 1439813272
Total Pages : 284 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Multivariate Generalized Linear Mixed Models Using R by : Damon Mark Berridge

Download or read book Multivariate Generalized Linear Mixed Models Using R written by Damon Mark Berridge and published by CRC Press. This book was released on 2011-04-25 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate Generalized Linear Mixed Models Using R presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R.A Un

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.