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A Boosting Approach To High Dimensional Linear Mixed Model
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Book Synopsis A Boosting Approach to High Dimensional Linear Mixed Model by : Haoyang Fan
Download or read book A Boosting Approach to High Dimensional Linear Mixed Model written by Haoyang Fan and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the growing need in biomedical and sociology research, longitudinal data are attracting more and more researchers. In these studies, data are usually collected over time across different subjects. Longitudinal and panel data offer us many opportunities to study the correlations between variables and model changes over time. In past decades, linear mixed models have been successfully used to analyze longitudinal and panel data. Linear mixed model can not only describe the data trajectory but also model the dependence across subjects. However, with the advent of modern technology, modeling, inference and interpretation of linear mixed models are greatly challenged by the high dimension of fixed and random effects in many longitudinal and panel data. In this dissertation, I propose a new boosting estimate to fit high dimensional linear mixed model. The theoretical properties of the boosting approach are well studied. Under mild conditions, asymptotic consistency of fixed effects estimate in our boosting framework does not depend on random effects estimate, structures and underlying distributions in high dimensional linear mixed model. The asymptotic consistency is also guaranteed when the dimension of covariates for both fixed and random effects diverging to infinity as sample size increasing. Simulations and real data analysis are also provided to demonstrate advantages of proposed boosting approach comparing to some existing methods.
Book Synopsis Linear and Generalized Linear Mixed Models and Their Applications by : Jiming Jiang
Download or read book Linear and Generalized Linear Mixed Models and Their Applications written by Jiming Jiang and published by Springer Nature. This book was released on 2021-03-22 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.
Book Synopsis Statistics for High-Dimensional Data by : Peter Bühlmann
Download or read book Statistics for High-Dimensional Data written by Peter Bühlmann and published by Springer Science & Business Media. This book was released on 2011-06-08 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.
Book Synopsis Boosting for High-dimensional Linear Models by : Peter Lukas Bühlmann (Mathématicien)
Download or read book Boosting for High-dimensional Linear Models written by Peter Lukas Bühlmann (Mathématicien) and published by . This book was released on 2004 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Modelling and Regression Structures by : Thomas Kneib
Download or read book Statistical Modelling and Regression Structures written by Thomas Kneib and published by Springer Science & Business Media. This book was released on 2010-01-12 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions collected in this book have been written by well-known statisticians to acknowledge Ludwig Fahrmeir's far-reaching impact on Statistics as a science, while celebrating his 65th birthday. The contributions cover broad areas of contemporary statistical model building, including semiparametric and geoadditive regression, Bayesian inference in complex regression models, time series modelling, statistical regularization, graphical models and stochastic volatility models.
Book Synopsis Linear and Generalized Linear Mixed Models and Their Applications: Linear Mixed Models: Part II by : Jiming Jiang
Download or read book Linear and Generalized Linear Mixed Models and Their Applications: Linear Mixed Models: Part II written by Jiming Jiang and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this book covers two major classes of mixed effects models-linear mixed models and generalized linear mixed models-and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. It offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it discusses the latest developments and methods in the field, incorporating relevant updates since publication of the first edition. These include advances in high-dimensional linear mixed models in genome-wide association studies (GWAS), advances in inference about generalized linear mixed models with crossed random effects, new methods in mixed model prediction, mixed model selection, and mixed model diagnostics. This book is suitable for students, researchers, and practitioners who are interested in using mixed models for statistical data analysis with public health applications. It is best for graduate courses in statistics, or for those who have taken a first course in mathematical statistics, are familiar with using computers for data analysis, and have a foundational background in calculus and linear algebra.
Book Synopsis Robust Mixed Model Analysis by : Jiang Jiming
Download or read book Robust Mixed Model Analysis written by Jiang Jiming and published by World Scientific. This book was released on 2019-04-10 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed-effects models have found broad applications in various fields. As a result, the interest in learning and using these models is rapidly growing. On the other hand, some of these models, such as the linear mixed models and generalized linear mixed models, are highly parametric, involving distributional assumptions that may not be satisfied in real-life problems. Therefore, it is important, from a practical standpoint, that the methods of inference about these models are robust to violation of model assumptions. Fortunately, there is a full scale of methods currently available that are robust in certain aspects. Learning about these methods is essential for the practice of mixed-effects models.This research monograph provides a comprehensive account of methods of mixed model analysis that are robust in various aspects, such as to violation of model assumptions, or to outliers. It is suitable as a reference book for a practitioner who uses the mixed-effects models, and a researcher who studies these models. It can also be treated as a graduate text for a course on mixed-effects models and their applications.
Book Synopsis Generalized Linear Mixed Models by : Charles E. McCulloch
Download or read book Generalized Linear Mixed Models written by Charles E. McCulloch and published by IMS. This book was released on 2003 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wiley Series in Probability and Statistics A modern perspective on mixed models The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data. As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features: * A review of the basics of linear models and linear mixed models * Descriptions of models for nonnormal data, including generalized linear and nonlinear models * Analysis and illustration of techniques for a variety of real data sets * Information on the accommodation of longitudinal data using these models * Coverage of the prediction of realized values of random effects * A discussion of the impact of computing issues on mixed models
Book Synopsis Developments in Statistical Modelling by : Jochen Einbeck
Download or read book Developments in Statistical Modelling written by Jochen Einbeck and published by Springer Nature. This book was released on with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High-dimensional Gaussian and Generalized Linear Mixed Models by : Jürg Schelldorfer
Download or read book High-dimensional Gaussian and Generalized Linear Mixed Models written by Jürg Schelldorfer and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data by : Syed Ejaz Ahmed
Download or read book Post-Shrinkage Strategies in Statistical and Machine Learning for High Dimensional Data written by Syed Ejaz Ahmed and published by CRC Press. This book was released on 2023-05-25 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some post-estimation and predictions strategies for the host of useful statistical models with applications in data science. It combines statistical learning and machine learning techniques in a unique and optimal way. It is well-known that machine learning methods are subject to many issues relating to bias, and consequently the mean squared error and prediction error may explode. For this reason, we suggest shrinkage strategies to control the bias by combining a submodel selected by a penalized method with a model with many features. Further, the suggested shrinkage methodology can be successfully implemented for high dimensional data analysis. Many researchers in statistics and medical sciences work with big data. They need to analyse this data through statistical modelling. Estimating the model parameters accurately is an important part of the data analysis. This book may be a repository for developing improve estimation strategies for statisticians. This book will help researchers and practitioners for their teaching and advanced research, and is an excellent textbook for advanced undergraduate and graduate courses involving shrinkage, statistical, and machine learning. The book succinctly reveals the bias inherited in machine learning method and successfully provides tools, tricks and tips to deal with the bias issue. Expertly sheds light on the fundamental reasoning for model selection and post estimation using shrinkage and related strategies. This presentation is fundamental, because shrinkage and other methods appropriate for model selection and estimation problems and there is a growing interest in this area to fill the gap between competitive strategies. Application of these strategies to real life data set from many walks of life. Analytical results are fully corroborated by numerical work and numerous worked examples are included in each chapter with numerous graphs for data visualization. The presentation and style of the book clearly makes it accessible to a broad audience. It offers rich, concise expositions of each strategy and clearly describes how to use each estimation strategy for the problem at hand. This book emphasizes that statistics/statisticians can play a dominant role in solving Big Data problems, and will put them on the precipice of scientific discovery. The book contributes novel methodologies for HDDA and will open a door for continued research in this hot area. The practical impact of the proposed work stems from wide applications. The developed computational packages will aid in analyzing a broad range of applications in many walks of life.
Book Synopsis LINEAR MIXED MODEL SELECTION BY PARTIAL CORRELATION by : Audry Alabiso
Download or read book LINEAR MIXED MODEL SELECTION BY PARTIAL CORRELATION written by Audry Alabiso and published by . This book was released on 2020 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear mixed models (LMM) are commonly used when observations are no longer independent of each other, and instead, clustered into two or more groups. In the LMM, the mean response for each subject is modeled by a combination of fixed effects and random effects. The fixed effects are characteristics shared by all individuals in the study; they are analogous to the coefficients of the linear model. The random effects are specific to each group or cluster and help describe the correlation structure of the observations. Because of this, linear mixed models are popular when multiple measurements are made on the same subject or when there is a natural clustering or grouping of observations. Our goal in this dissertation is to perform fixed effect selection in the high-dimensional linear mixed model. We generally define high-dimensional data to be when the number of potential predictors is large relative to the sample size. High-dimensional data is common in genomic and other biological datasets. In the high-dimensional setting, selecting the fixed effect coefficients can be difficult due to the number of potential models to choose from. However, it is important to be able to do so in order to build models that are easy to interpret. Many current techniques for fixed effect selection in the high-dimensional LMM are based on the penalized log likelihood. However, adding a penalized term to the log likelihood results in a non-convex optimization problem which requires numerical methods to solve and a data dependent tuning parameter to select the amount of regularization. In contrast to the penalized likelihood, the partial correlation is based on the marginal measures of association between each predictor and the conditioned response. Techniques based on the partial correlation have two main advantages to those based on penalized likelihoods: no data dependent tuning parameter is required to select the fixed effects and the partial correlation is not influenced by strong correlation between covariates. In this dissertation we propose using the partial correlation between the response variable conditioned on the random effects to select fixed effects in the LMM. This is an extension of variable selection using partial correlation developed by Bühlmann, Kalisch, and Maathuis (2010) to the linear mixed model by conditioning the response variable on the random effects. At the time of this writing, selection methods using partial correlation have not been attempted to select fixed effects in the linear mixed model. This dissertation proposes a two stage procedure for selecting the fixed effects in the high-dimensional linear mixed model. In the first stage, we use the partial correlation to perform an initial fixed effect variable screening procedure in order to estimate an initial linear mixed model. In the second stage, we use the initial linear mixed model to predict the values of the random effects using the Best Linear Unbiased Predictor (BLUP). These predicted values are used to condition the response variable by subtracting the group-specific random effects from the response. After conditioning on the random effects, the observations are effectively independent, and we select variables using the partial correlation between the covariates and the conditioned response. In this dissertation, we show that this procedure consistently selects fixed effects in the linear mixed model. To use the partial correlation to select variables in the LMM, we require the assumption of partial faithfulness on the design matrix X. The partial faithfulness assumption in the LMM describes the relationship between the response conditioned on the random effects and the coefficients of the fixed effects of the LMM. Partial faithfulness in the LMM says that the fixed effect coefficient is equal to zero if and only if the partial correlation between the conditioned response and a predictor under consideration is equal to zero for some set of controlling variables. We present theoretical results that demonstrate that when partial faithfulness holds for the LMM, the relationship between the partial correlation and the coefficients of the fixed effects holds. We investigate the performance of this method in a variety of simulated high-dimensional scenarios, including non-normal distributions of the random effects. We find that the method is effective at selecting the active set of variables even in the presence of many covariates. Through these simulations, we observe that the proposed technique selects variables quickly and with few false positives, especially in the case where the covariates are highly correlated with each other. We also apply the method to a real high-dimensional dataset regarding the production of riboflavin.
Book Synopsis Sustainable Statistical and Data Science Methods and Practices by : O. Olawale Awe
Download or read book Sustainable Statistical and Data Science Methods and Practices written by O. Olawale Awe and published by Springer Nature. This book was released on 2024-01-05 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers papers presented at the LISA 2020 Sustainability Symposium in Kumasi, Ghana, May 2–6, 2022. They focus on sustainable methods and practices of using statistics and data science to address real-world problems. From utilizing social media for statistical collaboration to predicting obesity among rural women, and from analyzing inflation in Nigeria using machine learning to teaching data science in Africa, this book explores the intersection of data, statistics, and sustainability. With practical applications, code snippets, and case studies, this book offers valuable insights for researchers, policymakers, and data enthusiasts alike. The LISA 2020 Global Network aims to enhance statistical and data science capability in developing countries through the creation of a network of collaboration laboratories (also known as “stat labs”). These stat labs are intended to serve as engines for development by training the next generation of collaborative statisticians and data scientists, providing research infrastructure for researchers, data producers, and decision-makers, and enabling evidence-based decision-making that has a positive impact on society. The research conducted at LISA 2020 focuses on practical methods and applications for sustainable growth of statistical capacity in developing nations.
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis DAGStat 2022 by : DAGStat (Deutsche Arbeitsgemeinschaft Statistik)
Download or read book DAGStat 2022 written by DAGStat (Deutsche Arbeitsgemeinschaft Statistik) and published by Cuvillier Verlag. This book was released on 2022-03-16 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Das Buch enthält die Abstracts der eingeladenen bzw. angenommenen Vorträge der 6. Konferenz der Deutschen Arbeitsgemeinschaft Statistik (DAGStat), welche vom 28. März bis 1. April 2022 am Universitätsklinikum Hamburg-Eppendorf (UKE) in Kooperation mit der Universität Hamburg sowie der Helmut-Schmidt-Universität stattfand. Die Konferenz stellte ebenfalls das 68. Biometrische Kolloquium der Deutschen Region der International Biometric Society (IBS-DR) dar, sowie die 45. Jahrestagung der Gesellschaft für Klassifikation (GfKl/Data Science Society). Die Vorträge behandelten dabei ein breites Spektrum sowohl angewandter als auch eher methodischer/theoretischer Themen aus dem Bereich Statistik und Data Science.
Book Synopsis Models for Discrete Longitudinal Data by : Geert Molenberghs
Download or read book Models for Discrete Longitudinal Data written by Geert Molenberghs and published by Springer Science & Business Media. This book was released on 2006-08-30 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear mixed model has become the main parametric tool for the analysis of continuous longitudinal data, as the authors discussed in their 2000 book. Without putting too much emphasis on software, the book shows how the different approaches can be implemented within the SAS software package. The authors received the American Statistical Association's Excellence in Continuing Education Award based on short courses on longitudinal and incomplete data at the Joint Statistical Meetings of 2002 and 2004.
Book Synopsis Introduction to High-Dimensional Statistics by : Christophe Giraud
Download or read book Introduction to High-Dimensional Statistics written by Christophe Giraud and published by CRC Press. This book was released on 2021-08-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the first edition: "[This book] succeeds singularly at providing a structured introduction to this active field of research. ... it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. ... recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research." —Journal of the American Statistical Association Introduction to High-Dimensional Statistics, Second Edition preserves the philosophy of the first edition: to be a concise guide for students and researchers discovering the area and interested in the mathematics involved. The main concepts and ideas are presented in simple settings, avoiding thereby unessential technicalities. High-dimensional statistics is a fast-evolving field, and much progress has been made on a large variety of topics, providing new insights and methods. Offering a succinct presentation of the mathematical foundations of high-dimensional statistics, this new edition: Offers revised chapters from the previous edition, with the inclusion of many additional materials on some important topics, including compress sensing, estimation with convex constraints, the slope estimator, simultaneously low-rank and row-sparse linear regression, or aggregation of a continuous set of estimators. Introduces three new chapters on iterative algorithms, clustering, and minimax lower bounds. Provides enhanced appendices, minimax lower-bounds mainly with the addition of the Davis-Kahan perturbation bound and of two simple versions of the Hanson-Wright concentration inequality. Covers cutting-edge statistical methods including model selection, sparsity and the Lasso, iterative hard thresholding, aggregation, support vector machines, and learning theory. Provides detailed exercises at the end of every chapter with collaborative solutions on a wiki site. Illustrates concepts with simple but clear practical examples.
