Download or read book Stationary Sequences and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.

Download or read book Regression Analysis Under A Priori Parameter Restrictions written by Pavel S. Knopov and published by Springer Science & Business Media. This book was released on 2011-09-28 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance

Download or read book Weakly Stationary Random Fields Invariant Subspaces and Applications written by Vidyadhar S. Mandrekar and published by CRC Press. This book was released on 2017-11-20 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory.

Download or read book Gaussian and Non Gaussian Linear Time Series and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.

Download or read book Empirical Estimates in Stochastic Optimization and Identification written by Pavel S. Knopov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains problems of stochastic optimization and identification. Results concerning uniform law of large numbers, convergence of approximate estimates of extreme points, as well as empirical estimates of functionals with probability 1 and in probability are presented. Audience: Specialists in stochastic optimization and estimations, postgraduate students, and graduate students studying such topics

Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nicolai Leonenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. The first chapter treats basic concepts of the spectral theory of random fields, some important examples of random processes and fields with singular spectrum, and Tauberian and Abelian theorems for covariance function of long-memory random fields. Chapter 2 is devoted to limit theorems for spherical averages of nonlinear transformations of Gaussian and chi-square random fields. Chapter 3 summarises some limit theorems for geometric type functionals of random fields. Limit theorems for the solutions of Burgers' equation with random data via parabolic and hyperbolic rescaling are demonstrated in Chapter 4. Lastly, Chapter 5 deals with some problems for statistical analysis of random fields with singular spectrum. Audience: This book will be of interest to mathematicians who use random fields in engineering or other applications.

Download or read book Statistical Analysis of Random Fields written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 1989-07-31 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, ...* si j'avait su comment en revcnir. One service mathematics has rendered the je n'y scrais point aile.' human race. It has put common sense back where it belongs, on the topmost shclf next Jules Verne to the dusty canister labdlcd 'discarded non· The series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Download or read book Parameter Estimation in Stochastic Differential Equations written by Jaya P. N. Bishwal and published by Springer. This book was released on 2007-09-26 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Download or read book Statistical Methods for Spatial Data Analysis written by Oliver Schabenberger and published by CRC Press. This book was released on 2017-01-27 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.

Download or read book Dependence in Probability and Statistics written by Patrice Bertail and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an account of recent developments in the field of probability and statistics for dependent data. It covers a wide range of topics from Markov chain theory and weak dependence with an emphasis on some recent developments on dynamical systems, to strong dependence in times series and random fields. There is a section on statistical estimation problems and specific applications. The book is written as a succession of papers by field specialists, alternating general surveys, mostly at a level accessible to graduate students in probability and statistics, and more general research papers mainly suitable to researchers in the field.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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Download or read book Statistical Signal Processing written by Swagata Nandi and published by Springer Nature. This book was released on 2020-08-21 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to various signal processing models that have been used in analyzing periodic data, and discusses the statistical and computational methods involved. Signal processing can broadly be considered to be the recovery of information from physical observations. The received signals are usually disturbed by thermal, electrical, atmospheric or intentional interferences, and due to their random nature, statistical techniques play an important role in their analysis. Statistics is also used in the formulation of appropriate models to describe the behavior of systems, the development of appropriate techniques for estimation of model parameters and the assessment of the model performances. Analyzing different real-world data sets to illustrate how different models can be used in practice, and highlighting open problems for future research, the book is a valuable resource for senior undergraduate and graduate students specializing in mathematics or statistics.

Download or read book Pattern Theory written by Ulf Grenander and published by Oxford University Press. This book was released on 2007 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Functional and High Dimensional Statistics and Related Fields written by Germán Aneiros and published by Springer Nature. This book was released on 2020-06-19 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the latest research on the statistical analysis of functional, high-dimensional and other complex data, addressing methodological and computational aspects, as well as real-world applications. It covers topics like classification, confidence bands, density estimation, depth, diagnostic tests, dimension reduction, estimation on manifolds, high- and infinite-dimensional statistics, inference on functional data, networks, operatorial statistics, prediction, regression, robustness, sequential learning, small-ball probability, smoothing, spatial data, testing, and topological object data analysis, and includes applications in automobile engineering, criminology, drawing recognition, economics, environmetrics, medicine, mobile phone data, spectrometrics and urban environments. The book gathers selected, refereed contributions presented at the Fifth International Workshop on Functional and Operatorial Statistics (IWFOS) in Brno, Czech Republic. The workshop was originally to be held on June 24-26, 2020, but had to be postponed as a consequence of the COVID-19 pandemic. Initiated by the Working Group on Functional and Operatorial Statistics at the University of Toulouse in 2008, the IWFOS workshops provide a forum to discuss the latest trends and advances in functional statistics and related fields, and foster the exchange of ideas and international collaboration in the field.

Download or read book Handbook of Spatial Statistics written by Alan E. Gelfand and published by CRC Press. This book was released on 2010-03-19 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assembling a collection of very prominent researchers in the field, the Handbook of Spatial Statistics presents a comprehensive treatment of both classical and state-of-the-art aspects of this maturing area. It takes a unified, integrated approach to the material, providing cross-references among chapters.The handbook begins with a historical intro