Download or read book On Robust Estimation of Multiple Change Points in Multivariate and Matrix Processes written by Yana Melnykov and published by . This book was released on 2017 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are numerous areas of human activities where various processes are observed over time. If the conditions of the process change, it can be reflected through the shift in observed response values. The detection and estimation of such shifts is commonly known as change point inference. While the estimation helps us learn about the process nature, assess its parameters, and analyze identified change points, the detection focuses on finding shifts in the real-time process flow. There is a vast variety of methods proposed in the literature to target change point detections in both settings. Unfortunately, the majority of procedures impose very restrictive assumptions. Some of them include the normality of data, independence of observations, or independence of subjects in multisubject studies. In this dissertation, a new methodology, relying on more realistic assumptions, is developed. This dissertation report includes three chapters. The summary of each chapter is provided below. In the first chapter, we develop methodology capable of estimating and detecting multiple change points in a multisubject single variable process observed over time. In the second chapter, we introduce methodology for the robust estimation of change points in multivariate processes observed over time. In the third chapter, we generalize the ideas presented in the first two chapters by developing methodology capable of identifying multiple change points in multisubject matrix processes observed over time.
Download or read book Innovations in Multivariate Statistical Modeling written by Andriëtte Bekker and published by Springer Nature. This book was released on 2022-12-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate statistical analysis has undergone a rich and varied evolution during the latter half of the 20th century. Academics and practitioners have produced much literature with diverse interests and with varying multidisciplinary knowledge on different topics within the multivariate domain. Due to multivariate algebra being of sustained interest and being a continuously developing field, its appeal breaches laterally across multiple disciplines to act as a catalyst for contemporary advances, with its core inferential genesis remaining in that of statistics. It is exactly this varied evolution caused by an influx in data production, diffusion, and understanding in scientific fields that has blurred many lines between disciplines. The cross-pollination between statistics and biology, engineering, medical science, computer science, and even art, has accelerated the vast amount of questions that statistical methodology has to answer and report on. These questions are often multivariate in nature, hoping to elucidate uncertainty on more than one aspect at the same time, and it is here where statistical thinking merges mathematical design with real life interpretation for understanding this uncertainty. Statistical advances benefit from these algebraic inventions and expansions in the multivariate paradigm. This contributed volume aims to usher novel research emanating from a multivariate statistical foundation into the spotlight, with particular significance in multidisciplinary settings. The overarching spirit of this volume is to highlight current trends, stimulate a focus on, and connect multidisciplinary dots from and within multivariate statistical analysis. Guided by these thoughts, a collection of research at the forefront of multivariate statistical thinking is presented here which has been authored by globally recognized subject matter experts.
Download or read book Theory and Applications of Recent Robust Methods written by Mia Hubert and published by Birkhäuser. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for both researchers and practitioners, this book will be a valuable resource for studying and applying recent robust statistical methods. It contains up-to-date research results in the theory of robust statistics Treats computational aspects and algorithms and shows interesting and new applications.
Download or read book Matrix Based Introduction to Multivariate Data Analysis written by Kohei Adachi and published by Springer Nature. This book was released on 2020-05-20 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook that allows readers who may be unfamiliar with matrices to understand a variety of multivariate analysis procedures in matrix forms. By explaining which models underlie particular procedures and what objective function is optimized to fit the model to the data, it enables readers to rapidly comprehend multivariate data analysis. Arranged so that readers can intuitively grasp the purposes for which multivariate analysis procedures are used, the book also offers clear explanations of those purposes, with numerical examples preceding the mathematical descriptions. Supporting the modern matrix formulations by highlighting singular value decomposition among theorems in matrix algebra, this book is useful for undergraduate students who have already learned introductory statistics, as well as for graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis. The book begins by explaining fundamental matrix operations and the matrix expressions of elementary statistics. Then, it offers an introduction to popular multivariate procedures, with each chapter featuring increasing advanced levels of matrix algebra. Further the book includes in six chapters on advanced procedures, covering advanced matrix operations and recently proposed multivariate procedures, such as sparse estimation, together with a clear explication of the differences between principal components and factor analyses solutions. In a nutshell, this book allows readers to gain an understanding of the latest developments in multivariate data science.
Download or read book Mathematical Tools for Applied Multivariate Analysis written by Paul E. Green and published by Academic Press. This book was released on 2014-05-10 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students.
Download or read book Robust and Multivariate Statistical Methods written by Mengxi Yi and published by Springer Nature. This book was released on 2023-04-19 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
Download or read book Applied Bayesian Hierarchical Methods written by Peter D. Congdon and published by CRC Press. This book was released on 2010-05-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach
Download or read book Statistical Learning for Big Dependent Data written by Daniel Peña and published by John Wiley & Sons. This book was released on 2021-03-02 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master advanced topics in the analysis of large, dynamically dependent datasets with this insightful resource Statistical Learning with Big Dependent Data delivers a comprehensive presentation of the statistical and machine learning methods useful for analyzing and forecasting large and dynamically dependent data sets. The book presents automatic procedures for modelling and forecasting large sets of time series data. Beginning with some visualization tools, the book discusses procedures and methods for finding outliers, clusters, and other types of heterogeneity in big dependent data. It then introduces various dimension reduction methods, including regularization and factor models such as regularized Lasso in the presence of dynamical dependence and dynamic factor models. The book also covers other forecasting procedures, including index models, partial least squares, boosting, and now-casting. It further presents machine-learning methods, including neural network, deep learning, classification and regression trees and random forests. Finally, procedures for modelling and forecasting spatio-temporal dependent data are also presented. Throughout the book, the advantages and disadvantages of the methods discussed are given. The book uses real-world examples to demonstrate applications, including use of many R packages. Finally, an R package associated with the book is available to assist readers in reproducing the analyses of examples and to facilitate real applications. Analysis of Big Dependent Data includes a wide variety of topics for modeling and understanding big dependent data, like: New ways to plot large sets of time series An automatic procedure to build univariate ARMA models for individual components of a large data set Powerful outlier detection procedures for large sets of related time series New methods for finding the number of clusters of time series and discrimination methods , including vector support machines, for time series Broad coverage of dynamic factor models including new representations and estimation methods for generalized dynamic factor models Discussion on the usefulness of lasso with time series and an evaluation of several machine learning procedure for forecasting large sets of time series Forecasting large sets of time series with exogenous variables, including discussions of index models, partial least squares, and boosting. Introduction of modern procedures for modeling and forecasting spatio-temporal data Perfect for PhD students and researchers in business, economics, engineering, and science: Statistical Learning with Big Dependent Data also belongs to the bookshelves of practitioners in these fields who hope to improve their understanding of statistical and machine learning methods for analyzing and forecasting big dependent data.
Download or read book Multivariate Analysis of Variance and Robust Estimation of Covariance Structures when the Data are Curves written by Minggao Shi and published by . This book was released on 1993 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Correlation written by Georgy L. Shevlyakov and published by John Wiley & Sons. This book was released on 2016-09-19 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This bookpresents material on both the analysis of the classical concepts of correlation and on the development of their robust versions, as well as discussing the related concepts of correlation matrices, partial correlation, canonical correlation, rank correlations, with the corresponding robust and non-robust estimation procedures. Every chapter contains a set of examples with simulated and real-life data. Key features: Makes modern and robust correlation methods readily available and understandable to practitioners, specialists, and consultants working in various fields. Focuses on implementation of methodology and application of robust correlation with R. Introduces the main approaches in robust statistics, such as Huber’s minimax approach and Hampel’s approach based on influence functions. Explores various robust estimates of the correlation coefficient including the minimax variance and bias estimates as well as the most B- and V-robust estimates. Contains applications of robust correlation methods to exploratory data analysis, multivariate statistics, statistics of time series, and to real-life data. Includes an accompanying website featuring computer code and datasets Features exercises and examples throughout the text using both small and large data sets. Theoretical and applied statisticians, specialists in multivariate statistics, robust statistics, robust time series analysis, data analysis and signal processing will benefit from this book. Practitioners who use correlation based methods in their work as well as postgraduate students in statistics will also find this book useful.
Download or read book Analyzing Multivariate Data written by Norman Cliff and published by . This book was released on 1987 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Robust Estimation of Multivariate Location and Scale in the Presence of Asymmetry microform written by Douglas P. Wiens and published by National Library of Canada. This book was released on 1982 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multivariate Analysis of Variance written by James H. Bray and published by SAGE. This book was released on 1985 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bray's monograph considers the multivariate form of analysis of variance (MANOVA). It is a technique which can be used in such different academic disciplines as psychology, sociology, biology, and education.
Download or read book Robust Statistics written by Frank R. Hampel and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selectedbooks that have been made more accessible to consumers in an effortto increase global appeal and general circulation. With these newunabridged softcover volumes, Wiley hopes to extend the lives ofthese works by making them available to future generations ofstatisticians, mathematicians, and scientists. "This is a nice book containing a wealth of information, much ofit due to the authors. . . . If an instructor designing such acourse wanted a textbook, this book would be the best choiceavailable. . . . There are many stimulating exercises, and the bookalso contains an excellent index and an extensive list ofreferences." —Technometrics "[This] book should be read carefully by anyone who isinterested in dealing with statistical models in a realisticfashion." —American Scientist Introducing concepts, theory, and applications, RobustStatistics is accessible to a broad audience, avoidingallusions to high-powered mathematics while emphasizing ideas,heuristics, and background. The text covers the approach based onthe influence function (the effect of an outlier on an estimater,for example) and related notions such as the breakdown point. Italso treats the change-of-variance function, fundamental conceptsand results in the framework of estimation of a single parameter,and applications to estimation of covariance matrices andregression parameters.
Download or read book Statistical Process Monitoring Using Advanced Data Driven and Deep Learning Approaches written by Fouzi Harrou and published by Elsevier. This book was released on 2020-07-03 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Process Monitoring Using Advanced Data-Driven and Deep Learning Approaches tackles multivariate challenges in process monitoring by merging the advantages of univariate and traditional multivariate techniques to enhance their performance and widen their practical applicability. The book proceeds with merging the desirable properties of shallow learning approaches – such as a one-class support vector machine and k-nearest neighbours and unsupervised deep learning approaches – to develop more sophisticated and efficient monitoring techniques. Finally, the developed approaches are applied to monitor many processes, such as waste-water treatment plants, detection of obstacles in driving environments for autonomous robots and vehicles, robot swarm, chemical processes (continuous stirred tank reactor, plug flow rector, and distillation columns), ozone pollution, road traffic congestion, and solar photovoltaic systems. - Uses a data-driven based approach to fault detection and attribution - Provides an in-depth understanding of fault detection and attribution in complex and multivariate systems - Familiarises you with the most suitable data-driven based techniques including multivariate statistical techniques and deep learning-based methods - Includes case studies and comparison of different methods
Download or read book Principles of Multivariate Analysis written by W. J. Krzanowski and published by Oxford University Press. This book was released on 2000-09-28 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate analysis is necessary whenever more than one characteristic is observed on each individual under study. Applications arise in very many areas of study. This book provides a comprehensive introduction to available techniques for analysing date of this form, written in a style that should appeal to non-specialists as well as to statisticians. In particular, geometric intuition is emphasized in preference to algebraic manipulation wherever possible. The new edition includes a survey of the most recent developments in the subject.
Download or read book Modern Nonparametric Robust and Multivariate Methods written by Klaus Nordhausen and published by Springer. This book was released on 2015-10-05 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading experts in the field, this edited volume brings together the latest findings in the area of nonparametric, robust and multivariate statistical methods. The individual contributions cover a wide variety of topics ranging from univariate nonparametric methods to robust methods for complex data structures. Some examples from statistical signal processing are also given. The volume is dedicated to Hannu Oja on the occasion of his 65th birthday and is intended for researchers as well as PhD students with a good knowledge of statistics.
