Описание: The book is concerned with linear time series and random fields in both the Gaussian and especially the non-Gaussian context. The principal focus is on
autoregressive moving average models and analogous random fields. Probabilistic and statistical questions are both discussed.
The Gaussian models are contrasted with
noncausal or noninvertible (nonminimum phase) non-Gaussian models which can have a much richer structure than Gaussian models. The book deals with problems of prediction
(which can have a nonlinear character) and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted.
The book is
intended as a text for graduate students in statistics, mathematics, engineering, the natural sciences and economics. An initial background in probability theory and statistics is
suggested. Notes on background, history and open problems are given at the end of the book.
Murray Rosenblatt is Professor of Mathematics at the University of California,
San Diego. He was a Guggenheim Fellow in 1965 and 1972 and is a member of the National Academy of Sciences, U.S.A. He is the author of Random Processes (1962), Markov
Processes: Structure and Asymptotic Behavior (1971), Stationary Sequences and Random Fields (1985), and Stochastic Curve Estimation (1991).
Описание: Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.?
Описание: This book presents some recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to handle a broader range of data types than those analyzed by traditional generalized linear models. One example is correlated angular data. This book provides a systematic treatment for the topic of estimating functions. Under this framework, both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to marginal models and mixed-effects models, this book covers topics on joint regression analysis based on Gaussian copulas and generalized state space models for longitudinal data from long time series.Various real-world data examples, numerical illustrations and software usage tips are presented throughout the book. This book has evolved from lecture notes on longitudinal data analysis, and may be considered suitable as a textbook for a graduate course on correlated data analysis. This book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications. Therefore, the book will serve as a useful reference for those who want theoretical explanations to puzzles arising from data analyses or deeper understanding of underlying theory related to analyses.
Описание: There are two main problems in statistics, estimation theory and hypothesis testing. For the classical finite-parametric case, these problems were studied in parallel. On the other hand, many statistical problems are not parametric in the classical sense; the objects of estimation or testing arefunctions, images, and so on. These can be treated as unknown infinite-dimensional parameters that belongto specific functional sets. This approach to nonparametric estimation under asymptotically minimax setting was started in the 1960s-1970s and was developed very intensively for wide classes of functional sets and loss functions.Nonparametric estimation problems have generated a large literature. On the other hand, nonparametrichypotheses testing problems have not drawn comparable attention in the statistical literature. In this book, the authors develop a modern theory of nonparametric goodness-of-fit testing. The presentation is based on an asymptotic version of the minimax approach. The key element of the theory isthe method of constructing of asymptotically least favorable priors for a wide enough class of nonparametric hypothesis testing problems. These provide methods for the construction of asymptotically optimal, rate optimal, and optimal adaptive test procedures. The book is addressed to mathematical statisticians who are interesting in the theory of nonparametricstatistical inference. It will be of interest to specialists who are dealing with applied nonparametric statistical problems in signal detection and transmission, and technical and mother fields. The material is suitable for graduate courses on mathematical statistics. The book assumes familiarity with probability theory.
Автор: Mandrekar Название: Stochastic Analysis For Gaussian Ra ISBN: 1498707815 ISBN-13(EAN): 9781498707817 Издательство: Taylor&Francis Рейтинг: Цена: 15426 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs).
The book begins with preliminary results on covariance and associated RKHS before introducing the Gaussian process and Gaussian random fields. The authors use chaos expansion to define the Skorokhod integral, which generalizes the It integral. They show how the Skorokhod integral is a dual operator of Skorokhod differentiation and the divergence operator of Malliavin. The authors also present Gaussian processes indexed by real numbers and obtain a Kallianpur-Striebel Bayes' formula for the filtering problem. After discussing the problem of equivalence and singularity of Gaussian random fields (including a generalization of the Girsanov theorem), the book concludes with the Markov property of Gaussian random fields indexed by measures and generalized Gaussian random fields indexed by Schwartz space. The Markov property for generalized random fields is connected to the Markov process generated by a Dirichlet form.
Описание: This proceedings volume contains eight selected papers thatwere presented in the International Symposium in Statistics (ISS) 2015 OnAdvances in Parametric and Semi-parametric Analysis of Multivariate, TimeSeries, Spatial-temporal, and Familial-longitudinal Data, held in St. John’s,Canada from July 6 to 8, 2015. The main objective of the ISS-2015 was thediscussion on advances and challenges in parametric and semi-parametric analysisfor correlated data in both continuous and discrete setups. Thus, as areflection of the theme of the symposium, the eight papers of this proceedingsvolume are presented in four parts. Part I is comprised of papers examiningElliptical t Distribution Theory. In Part II, the papers cover spatial andtemporal data analysis. Part III is focused on longitudinal multinomial modelsin parametric and semi-parametric setups. Finally Part IV concludes with apaper on the inferences for longitudinal data subject to a challenge ofimportant covariates selection from a set of large number of covariatesavailable for the individuals in the study.
Описание: This handbook brings together a comprehensive collection of mathematical material in one location. It also offers a variety of new results interpreted in a form that is particularly useful to engineers, scientists, and applied mathematicians.
Practitioners and researchers who have handled financial market data know that asset returns do not behave according to the bell-shaped curve, associated with the Gaussian or normal distribution. Indeed, the use of Gaussian models when the asset return distributions are not normal could lead to a wrong choice of portfolio, the underestimation of extreme losses or mispriced derivative products. Consequently, non-Gaussian models and models based on processes with jumps, are gaining popularity among financial market practitioners.
Non-Gaussian distributions are the key theme of this book which addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. One of the main aims is to bridge the gap between the theoretical developments and the practical implementations of what many users and researchers perceive as "sophisticated" models or black boxes. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series, such as exchange and interest rates.
The authors have taken care to make the material accessible to anyone with a basic knowledge of statistics, calculus and probability, while at the same time preserving the mathematical rigor and complexity of the original models.
This book will be an essential reference for practitioners in the finance industry, especially those responsible for managing portfolios and monitoring financial risk, but it will also be useful for mathematicians who want to know more about how their mathematical tools are applied in finance, and as a text for advanced courses in empirical finance; financial econometrics and financial derivatives.
Описание: This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum and then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.
Автор: Rue Название: Gaussian Markov Random Fields ISBN: 1584884320 ISBN-13(EAN): 9781584884323 Издательство: Taylor&Francis Рейтинг: Цена: 25410 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Gaussian Markov Random Field (GMRF) models, most widely used in spatial statistics are presented in this, the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects.
Автор: Bovier Название: Gaussian Processes on Trees ISBN: 1107160499 ISBN-13(EAN): 9781107160491 Издательство: Cambridge Academ Рейтинг: Цена: 9218 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.
Автор: Mandjes, Michel Название: Large deviations for gaussian queues ISBN: 0470015233 ISBN-13(EAN): 9780470015230 Издательство: Wiley Рейтинг: Цена: 17415 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Demonstrates how the Gaussian traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. This text provides an introduction to Gaussian queues, and surveys research into the modelling of communications networks. It is useful for postgraduate students in applied probability, and operations research.
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