Robust Mixtures Of Regression Models

Download Robust Mixtures Of Regression Models full books in PDF, epub, and Kindle. Read online Robust Mixtures Of Regression Models ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Robust Mixtures of Regression Models

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

DOWNLOAD NOW!

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.

Österreichisches UNIX Forum ; 5

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

DOWNLOAD NOW!

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:

Robust Mixture Regression Models Using T-distribution

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

DOWNLOAD NOW!

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.

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)

DOWNLOAD NOW!

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 Model Fitting by Laplace Distribution

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

DOWNLOAD NOW!

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.

Robust Mixture Linear EIV Regression Models by T-distribution

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

DOWNLOAD NOW!

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.

Robust Mixture Regression Modeling with Pearson Type VII Distribution

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

DOWNLOAD NOW!

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 Estimation of the Number of Components for Mixtures of Linear Regression

Author : Li Meng
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (883 download)

DOWNLOAD NOW!

Book Synopsis Robust Estimation of the Number of Components for Mixtures of Linear Regression by : Li Meng

Download or read book Robust Estimation of the Number of Components for Mixtures of Linear Regression written by Li Meng and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report, we investigate a robust estimation of the number of components in the mixture of regression models using trimmed information criterion. Compared to the traditional information criterion, the trimmed criterion is robust and not sensitive to outliers. The superiority of the trimmed methods in comparison with the traditional information criterion methods is illustrated through a simulation study. A real data application is also used to illustrate the effectiveness of the trimmed model selection methods.

Finite Mixture Models

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

DOWNLOAD NOW!

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.

Mixture Models

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

DOWNLOAD NOW!

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.

Robust Estimators for Finite Mixtures of Count Data Regression Models and Their Applications

Author : Ti-Jen Tsao
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (696 download)

DOWNLOAD NOW!

Book Synopsis Robust Estimators for Finite Mixtures of Count Data Regression Models and Their Applications by : Ti-Jen Tsao

Download or read book Robust Estimators for Finite Mixtures of Count Data Regression Models and Their Applications written by Ti-Jen Tsao and published by . This book was released on 2010 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Robust Multivariate Mixture Regression Models

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

DOWNLOAD NOW!

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.

Handbook of Mixture Analysis

Author : Sylvia Fruhwirth-Schnatter
Publisher : CRC Press
ISBN 13 : 0429508867
Total Pages : 388 pages
Book Rating : 4.4/5 (295 download)

DOWNLOAD NOW!

Book Synopsis Handbook of Mixture Analysis by : Sylvia Fruhwirth-Schnatter

Download or read book Handbook of Mixture Analysis written by Sylvia Fruhwirth-Schnatter and published by CRC Press. This book was released on 2019-01-04 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.

Optimal Mixture Experiments

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

DOWNLOAD NOW!

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.

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)

DOWNLOAD NOW!

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 Modeling

Author : Chun Yu
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (89 download)

DOWNLOAD NOW!

Book Synopsis Robust Mixture Modeling by : Chun Yu

Download or read book Robust Mixture Modeling written by Chun Yu and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. In this proposal, we first review and describe some available and popular robust techniques, including some recent developed ones, and compare them in terms of breakdown point and efficiency. In addition, we also use a simulation study and a real data application to compare the performance of existing robust methods under different scenarios. Finite mixture models are widely applied in a variety of random phenomena. However, inference of mixture models is a challenging work when the outliers exist in the data. The traditional maximum likelihood estimator (MLE) is sensitive to outliers. In this proposal, we propose a Robust Mixture via Mean shift penalization (RMM) in mixture models and Robust Mixture Regression via Mean shift penalization (RMRM) in mixture regression, to achieve simultaneous outlier detection and parameter estimation. A mean shift parameter is added to the mixture models, and penalized by a nonconvex penalty function. With this model setting, we develop an iterative thresholding embedded EM algorithm to maximize the penalized objective function. Comparing with other existing robust methods, the proposed methods show outstanding performance in both identifying outliers and estimating the parameters.

Statistical Learning for Large Dimensional Data by Finite Mixture Modeling

Author : Xiao Chen
Publisher :
ISBN 13 :
Total Pages : 125 pages
Book Rating : 4.:/5 (128 download)

DOWNLOAD NOW!

Book Synopsis Statistical Learning for Large Dimensional Data by Finite Mixture Modeling by : Xiao Chen

Download or read book Statistical Learning for Large Dimensional Data by Finite Mixture Modeling written by Xiao Chen and published by . This book was released on 2021 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of mixture modeling is to model the data as a mixture of processes or populations with distinct data patterns. l\lixture modeling can find combinations of hidden group memberships for many kinds of models. While mixture models based on Gaussian distributions still popular, they are sensitive to outliers and varying tails. Thus, robust mixture models are getting increasingly popular. In this thesis, we mainly considered replacing Gaussian density distributions with exponential power distributions in mixture modelling. The exponential power distribution is quite flex- ible: it can deal with both leptokurtic distributions and platykurtic distributions. In addition, the normal distribution is a particular case of EP distributions, which means that EP distributions allow continuous variation from being normal to non-normal. This thesis contributes to the mixture modeling in 3 ways. First, a family of mixtures of univariate exponential power distributions and a family of mixtures of multivariate exponential power distributions are considered. The EP mixture model is an attractive alternative to Gaussian mixture models and t mixture models in model-based clustering and density estimation. lt can deal with Gaussian, light- tailed, and heavy-tailed components at the same time. in this thesis, we used the penalty likelihood method proposed in Huang et al. 120171 to determine the number of components for mixtures of univariate power exponential distributions and mixtures of multivariate power exponential distributions, and we have proved the consistency of the order selection procedure. The proposed algorithm performs better than classical methods in order selection for EP mixture models, and it is not computing-intensive. Second, robust mixtures of regression models with EP distributions are introduced. These models provide a flexible framework for heterogeneous dependencies on the observed variables. Here we used the penalized log-likelihood for selecting the number of components. Simulations and real data analyses illustrate the robustness of the proposed model and the performance of the proposed penalized method in order selection. Lastly, we proposed mixtures of robust probabilistic principal component analyzers with EP distributions and proved the robustness of our method through toy examples and real data analysis. This method could model high-dimensional non-linear data using a combination of local linear models when there are outliers or heavy-tails. It could be used for high-dimensional clustering and data generation.