The Multivariate Student T Model in Robust Inference and Data Analysis PDF Download
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Author: Trevor S. Breusch
Publisher:
ISBN:
Category : Bayesian statistical decision theory
Languages : en
Pages : 36
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Book Description
Author: Trevor S. Breusch
Publisher:
ISBN:
Category : Bayesian statistical decision theory
Languages : en
Pages : 36
Get Book Here
Book Description
Author: A. K. Md. Ehsanes Saleh
Publisher: Wiley
ISBN: 9781118854051
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book summarizes the results of various models under normal theory with a brief review of the literature. Statistical Inference for Models with Multivariate t-Distributed Errors: Includes a wide array of applications for the analysis of multivariate observations Emphasizes the development of linear statistical models with applications to engineering, the physical sciences, and mathematics Contains an up-to-date bibliography featuring the latest trends and advances in the field to provide a collective source for research on the topic Addresses linear regression models with non-normal errors with practical real-world examples Uniquely addresses regression models in Student's t-distributed errors and t-models Supplemented with an Instructor's Solutions Manual, which is available via written request by the Publisher
Author: A. K. Md. Ehsanes Saleh
Publisher: John Wiley & Sons
ISBN: 1118853962
Category : Mathematics
Languages : en
Pages : 255
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Book Description
This book summarizes the results of various models under normal theory with a brief review of the literature. Statistical Inference for Models with Multivariate t-Distributed Errors: Includes a wide array of applications for the analysis of multivariate observations Emphasizes the development of linear statistical models with applications to engineering, the physical sciences, and mathematics Contains an up-to-date bibliography featuring the latest trends and advances in the field to provide a collective source for research on the topic Addresses linear regression models with non-normal errors with practical real-world examples Uniquely addresses regression models in Student's t-distributed errors and t-models Supplemented with an Instructor's Solutions Manual, which is available via written request by the Publisher
Author: Andrew Gelman
Publisher: CRC Press
ISBN: 1420057294
Category : Mathematics
Languages : en
Pages : 717
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Book Description
Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include: Stronger focus on MCMC Revision of the computational advice in Part III New chapters on nonlinear models and decision analysis Several additional applied examples from the authors' recent research Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more Reorganization of chapters 6 and 7 on model checking and data collection Bayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.
Author: Martin Bilodeau
Publisher: Springer Science & Business Media
ISBN: 0387226168
Category : Mathematics
Languages : en
Pages : 304
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Book Description
Intended as a textbook for students taking a first graduate course in the subject, as well as for the general reference of interested research workers, this text discusses, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, such as robust inference and the use of the bootstrap in a multivariate setting. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear algebra.
Author: Alvin C. Rencher
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 600
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Book Description
The most accessible introduction to the theory and practice of multivariate analysis Multivariate Statistical Inference and Applications is a user-friendly introduction to basic multivariate analysis theory and practice for statistics majors as well as nonmajors with little or no background in theoretical statistics. Among the many special features of this extremely accessible first text on multivariate analysis are: * Clear, step-by-step explanations of all key concepts and procedures along with original, easy-to-follow proofs * Numerous problems, examples, and tables of distributions * Many real-world data sets drawn from a wide range of disciplines * Reviews of univariate procedures that give rise to multivariate techniques * An extensive survey of the world literature on multivariate analysis * An in-depth review of matrix theory * A disk including all the data sets and SAS command files for all examples and numerical problems found in the book These same features also make Multivariate Statistical Inference and Applications an excellent professional resource for scientists and clinicians who need to acquaint themselves with multivariate techniques. It can be used as a stand-alone introduction or in concert with its more methods-oriented sibling volume, the critically acclaimed Methods of Multivariate Analysis.
Author: Aman Ullah
Publisher: Oxford University Press
ISBN: 0198774478
Category : Business & Economics
Languages : en
Pages : 241
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Book Description
This text provides a comprehensive treatment of finite sample statistics and econometrics. Within this framework, the book discusses the basic analytical tools of finite sample econometrics and explores their applications to models covered in a first year graduate course in econometrics.
Author: Brian Everitt
Publisher: Springer Science & Business Media
ISBN: 1441996508
Category : Mathematics
Languages : en
Pages : 284
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Book Description
The majority of data sets collected by researchers in all disciplines are multivariate, meaning that several measurements, observations, or recordings are taken on each of the units in the data set. These units might be human subjects, archaeological artifacts, countries, or a vast variety of other things. In a few cases, it may be sensible to isolate each variable and study it separately, but in most instances all the variables need to be examined simultaneously in order to fully grasp the structure and key features of the data. For this purpose, one or another method of multivariate analysis might be helpful, and it is with such methods that this book is largely concerned. Multivariate analysis includes methods both for describing and exploring such data and for making formal inferences about them. The aim of all the techniques is, in general sense, to display or extract the signal in the data in the presence of noise and to find out what the data show us in the midst of their apparent chaos. An Introduction to Applied Multivariate Analysis with R explores the correct application of these methods so as to extract as much information as possible from the data at hand, particularly as some type of graphical representation, via the R software. Throughout the book, the authors give many examples of R code used to apply the multivariate techniques to multivariate data.
Author: Linbo Liu
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Model robustness has become increasingly popular in recent decades. We study multiple aspects of robustness (in the setting of time series, image classification and linear regression) in this dissertation work. First three chapters concerns the time series setting. Specifically, Chapter 1 establishes a novel Bernstein-type inequality for high dimensional linear processes. We then apply it to investigate two high dimensional robust estimation problems: (1) time series regression with fat-tailed and correlated covariates and errors, (2) fat-tailed vector autoregression. As a natural requirement of consistency, the dimension can be allowed to increase exponentially with the sample size under very mild moment and dependence conditions. In Chapter 2, we develop Gaussian approximation theory for VAR model to derive the asymptotic distribution of the de-biased estimator and propose a multiplier bootstrap-assisted procedure to obtain critical values under very mild moment conditions on the innovations. Chapter 3 studies the threats of adversarial attack on multivariate probabilistic forecasting models and viable defense mechanisms. Our studies discover a new attack pattern that negatively impact the forecasting of a target time series via making strategic, sparse (imperceptible) modifications to the past observations of a small number of other time series. To mitigate the impact of such attack, we also develop two defense strategies. First, we extend a previously developed randomized smoothing technique in classification to multivariate forecasting scenarios. Second, we develop an adversarial training algorithm that learns to create adversarial examples and at the same time optimizes the forecasting model to improve its robustness against such adversarial simulation. In Chapter 4, we improve the robustness of image classifier by enhancing the randomized smoothing technique and model ensemble. Chapter 5 considers the robust estimation of linear regression coefficients under heavy-tailed noise and covariates using a clipping idea.
Author: Samuel Kotz
Publisher: Cambridge University Press
ISBN: 9780521826549
Category : Mathematics
Languages : en
Pages : 296
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Book Description
Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
