Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis

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Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis

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Author : György Terdik
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis written by György Terdik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

"Ninety percent of inspiration is perspiration. " [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of single-valued systems with memory for which a small per turbation of the input produces a small perturbation of the output. The Wiener functional series representation contains many transfer functions to describe entirely the input-output connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finite-order transfer functions (or the kernels) from a finite sam ple. One of the most important classes of stochastic systems, especially from a statistical point of view, is the case when all the transfer functions are determined by finitely many parameters. Therefore, one has to seek a finite-parameter nonlinear model which can adequately represent non linearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applica tions both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are de fined to be linear in both input and output only, when either the input or output are fixed. The bilinear model was introduced by Granger and Andersen [43] and Subba Rao [118], [119]. Terdik [126] gave the solution of xii a lower triangular bilinear model in terms of multiple Wiener-It(') integrals and gave a sufficient condition for the second order stationarity. An impor tant.

Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis

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Author : György Terdik
language : en
Publisher: Springer
Release Date : 1999-07-30

Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis written by György Terdik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-30 with Mathematics categories.

"Ninety percent of inspiration is perspiration. " [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of single-valued systems with memory for which a small per turbation of the input produces a small perturbation of the output. The Wiener functional series representation contains many transfer functions to describe entirely the input-output connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finite-order transfer functions (or the kernels) from a finite sam ple. One of the most important classes of stochastic systems, especially from a statistical point of view, is the case when all the transfer functions are determined by finitely many parameters. Therefore, one has to seek a finite-parameter nonlinear model which can adequately represent non linearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applica tions both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are de fined to be linear in both input and output only, when either the input or output are fixed. The bilinear model was introduced by Granger and Andersen [43] and Subba Rao [118], [119]. Terdik [126] gave the solution of xii a lower triangular bilinear model in terms of multiple Wiener-It(') integrals and gave a sufficient condition for the second order stationarity. An impor tant.

Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis

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Author : Gyorgy Terdik
language : en
Publisher:
Release Date : 1999-07-30

Bilinear Stochastic Models And Related Problems Of Nonlinear Time Series Analysis written by Gyorgy Terdik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-30 with categories.

The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-ItA integrals and finally chaotic Wiener-ItA spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.

An Introduction To Copulas

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Author : Roger B. Nelsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

An Introduction To Copulas written by Roger B. Nelsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

Noise Reduction By Wavelet Thresholding

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Author : Maarten Jansen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Noise Reduction By Wavelet Thresholding written by Maarten Jansen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

Wavelet methods have become a widely spread tool in signal and image process ing tasks. This book deals with statistical applications, especially wavelet based smoothing. The methods described in this text are examples of non-linear and non parametric curve fitting. The book aims to contribute to the field both among statis ticians and in the application oriented world (including but not limited to signals and images). Although it also contains extensive analyses of some existing methods, it has no intention whatsoever to be a complete overview of the field: the text would show too much bias towards my own algorithms. I rather present new material and own insights in the questions involved with wavelet based noise reduction. On the other hand, the presented material does cover a whole range of methodologies, and in that sense, the book may serve as an introduction into the domain of wavelet smoothing. Throughout the text, three main properties show up ever again: sparsity, locality and multiresolution. Nearly all wavelet based methods exploit at least one of these properties in some or the other way. These notes present research results of the Belgian Programme on Interuniver sity Poles of Attraction, initiated by the Belgian State, Prime Minister's Office for Science, Technology and Culture. The scientific responsibility rests with me. My research was financed by a grant (1995 - 1999) from the Flemish Institute for the Promotion of Scientific and Technological Research in the Industry (IWT).

Case Studies In Bayesian Statistics

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Author : Constantine Gatsonis
language : en
Publisher: Springer
Release Date : 2018-08-17

Case Studies In Bayesian Statistics written by Constantine Gatsonis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-17 with Mathematics categories.

The 6th Workshop on Case Studies in Bayesian Statistics was held at the Carnegie Mellon University in October, 2001. This volume contains the invited case studies with the accompanying discussion as well as contributed papers selected by a refereeing process.

Nonparametric Goodness Of Fit Testing Under Gaussian Models

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Author : Yuri Ingster
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-12

Nonparametric Goodness Of Fit Testing Under Gaussian Models written by Yuri Ingster and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-12 with Mathematics categories.

This book presents the modern theory of nonparametric goodness-of-fit testing. It fills the gap in modern nonparametric statistical theory by discussing hypothesis testing and addresses mathematical statisticians who are interesting in the theory of non-parametric statistical inference. It will be of interest to specialists who are dealing with applied non-parametric statistical problems relevant in signal detection and transmission and in technical and medical diagnostics among others.

Parametric And Nonparametric Inference From Record Breaking Data

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Author : Sneh Gulati
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Parametric And Nonparametric Inference From Record Breaking Data written by Sneh Gulati and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

As statisticians, we are constantly trying to make inferences about the underlying population from which data are observed. This includes estimation and prediction about the underlying population parameters from both complete and incomplete data. Recently, methodology for estimation and prediction from incomplete data has been found useful for what is known as "record-breaking data," that is, data generated from setting new records. There has long been a keen interest in observing all kinds of records-in particular, sports records, financial records, flood records, and daily temperature records, to mention a few. The well-known Guinness Book of World Records is full of this kind of record information. As usual, beyond the general interest in knowing the last or current record value, the statistical problem of prediction of the next record based on past records has also been an important area of record research. Probabilistic and statistical models to describe behavior and make predictions from record-breaking data have been developed only within the last fifty or so years, with a relatively large amount of literature appearing on the subject in the last couple of decades. This book, written from a statistician's perspective, is not a compilation of "records," rather, it deals with the statistical issues of inference from a type of incomplete data, record-breaking data, observed as successive record values (maxima or minima) arising from a phenomenon or situation under study. Prediction is just one aspect of statistical inference based on observed record values.

Linear Regression

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Author : Jürgen Groß
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Linear Regression written by Jürgen Groß and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The book covers the basic theory of linear regression models and presents a comprehensive survey of different estimation techniques as alternatives and complements to least squares estimation. Proofs are given for the most relevant results, and the presented methods are illustrated with the help of numerical examples and graphics. Special emphasis is placed on practicability and possible applications. The book is rounded off by an introduction to the basics of decision theory and an appendix on matrix algebra.

Ranked Set Sampling

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Author : Zehua Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Ranked Set Sampling written by Zehua Chen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

This monograph is the first book-length exposition of ranked set sampling. But, the subject matter is by no means new. The original notion of ranked set sampling, though not the technical term, was proposed by McIntyre in 1952. It was buried in the literature for quite a while. Its value was only re-discovered in recent years because of its cost-effective nature. Now, ranked set sampling has attracted practical interest in application areas such as agriculture, forestry, ecological and environmental science, and medical studies etc .. The theoretical foundations of the method has also been developed considerably, particularly during the last 15 years or so. A systematic exposition of the subject becomes necessary. This book covers every development of RSS since the birth of the original idea. Statistical inferences based on RSS are investigated from the originally intended estimation of a population mean to many more complicated pro cedures such as the inferences on smooth-function-of-means, quantiles and density functions, the distribution-free tests and regression analyses. Various variants of the original RSS scheme are explored, including RSS with imper fect judgment ranking or ranking by concomitant variables, adaptive RSS, multi-layer RSS and a variety of unbalanced RSS with certain optimalities.