Shrinkage Estimation for Mean and Covariance Matrices, Tsukuma Hisayuki, Kubokawa Tatsuya
Автор: Dominique Fourdrinier; William E. Strawderman; Mar Название: Shrinkage Estimation ISBN: 303002184X ISBN-13(EAN): 9783030021849 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides a coherent framework for understanding shrinkage estimation in statistics. The term refers to modifying a classical estimator by moving it closer to a target which could be known a priori or arise from a model. The goal is to construct estimators with improved statistical properties. The book focuses primarily on point and loss estimation of the mean vector of multivariate normal and spherically symmetric distributions.
Chapter 1 reviews the statistical and decision theoretic terminology and results that will be used throughout the book.
Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions.
Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports.
Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein’s identity doesn’t hold; Stein’s lemma and Stokes’ theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions.
Автор: S. Ejaz Ahmed Название: Penalty, Shrinkage and Pretest Strategies ISBN: 3319031481 ISBN-13(EAN): 9783319031484 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The objective of this book is to compare the statistical properties of penalty and non-penalty estimation strategies for some popular models.
Автор: Alice Guionnet Название: Large Random Matrices: Lectures on Macroscopic Asymptotics ISBN: 3540698965 ISBN-13(EAN): 9783540698968 Издательство: Springer Рейтинг: Цена: 6282.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Random matrix theory has developed in connection with various fields of mathematics and physics. This title includes notes that emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions.
Автор: James A. Mingo; Roland Speicher Название: Free Probability and Random Matrices ISBN: 1493983466 ISBN-13(EAN): 9781493983469 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 1. Asymptotic Freeness of Gaussian Random Matrices.- 2. The Free Central Limit Theorem and Free Cumulants.- 3. Free Harmonic Analysis.- 4. Asymptotic Freeness.- 5. Second Order Freeness.- 6. Free Group Factors and Freeness.- 7. Free Entropy X-the Microstates Approach via Large Deviations.- Free Entropy X*-the Non-Microstates Approach via Free Fisher Information.- 9. Operator-Valued Free Probability Theory and Block Random Matrices.- 10. Polynomials in Free Variables and Operator-Valued Convolution.- 11. Brown Measure.- Solutions to Exercises.- References.- Index of Exercises.
Автор: Gerold Alsmeyer; Matthias L?we Название: Random Matrices and Iterated Random Functions ISBN: 3642388051 ISBN-13(EAN): 9783642388057 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The aim of the workshop was to bring together researchers from two fields of probability theory: random matrix theory and the theory of iterated random functions.
Автор: Claude Dellacherie; Servet Martinez; Jaime San Mar Название: Inverse M-Matrices and Ultrametric Matrices ISBN: 3319102974 ISBN-13(EAN): 9783319102979 Издательство: Springer Рейтинг: Цена: 4890.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The study of M-matrices, their inverses and discrete potential theory is now a well-established part of linear algebra and the theory of Markov chains.
Автор: Pourahmadi Mohsen Название: High-dimensional Covariance Estimation ISBN: 1118034295 ISBN-13(EAN): 9781118034293 Издательство: Wiley Рейтинг: Цена: 12664.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Methods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences.
Автор: Blower, Gordon Название: Random matrices: high dimensional phenomena ISBN: 0521133122 ISBN-13(EAN): 9780521133128 Издательство: Cambridge Academ Рейтинг: Цена: 10138.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: An introduction to the behaviour of random matrices. Suitable for postgraduate students and non-experts.
Автор: Forrester Peter J Название: Log-Gases and Random Matrices ISBN: 0691128294 ISBN-13(EAN): 9780691128290 Издательство: Wiley Рейтинг: Цена: 20592.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Random matrix theory, both as an application and as a theory, has evolved rapidly over the years. This title chronicles these developments, emphasizing log-gases as a physical picture. It covers topics such as beta ensembles and Jack polynomials. It develops the application and theory of Gaussian and circular ensembles of random matrix theory.
Автор: Anderson, Greg W. Guionnet, Alice Zeitouni, Ofer Название: Introduction to random matrices ISBN: 0521194520 ISBN-13(EAN): 9780521194525 Издательство: Cambridge Academ Рейтинг: Цена: 11088.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The theory of random matrices plays an important role in many areas of pure mathematics. This rigorous introduction is specifically designed for graduate students in mathematics or related sciences, who have a background in probability theory but have not been exposed to advanced notions of functional analysis, algebra or geometry.
Описание: This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration.
Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.
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