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Author: T.S. Rao Publisher: Springer Science & Business Media ISBN: 1468463187 Category : Mathematics Languages : en Pages : 289
Book Description
The theory of time series models has been well developed over the last thirt,y years. Both the frequenc.y domain and time domain approaches have been widely used in the analysis of linear time series models. However. many physical phenomena cannot be adequately represented by linear models; hence the necessity of nonlinear models and higher order spectra. Recently a number of nonlinear models have been proposed. In this monograph we restrict attention to one particular nonlinear model. known as the "bilinear model". The most interesting feature of such a model is that its second order covariance analysis is ve~ similar to that for a linear model. This demonstrates the importance of higher order covariance analysis for nonlinear models. For bilinear models it is also possible to obtain analytic expressions for covariances. spectra. etc. which are often difficult to obtain for other proposed nonlinear models. Estimation of bispectrum and its use in the construction of tests for linearit,y and symmetry are also discussed. All the methods are illustrated with simulated and real data. The first author would like to acknowledge the benefit he received in the preparation of this monograph from delivering a series of lectures on the topic of bilinear models at the University of Bielefeld. Ecole Normale Superieure. University of Paris (South) and the Mathematisch Cen trum. Ams terdam.
Author: T.S. Rao Publisher: Springer Science & Business Media ISBN: 1468463187 Category : Mathematics Languages : en Pages : 289
Book Description
The theory of time series models has been well developed over the last thirt,y years. Both the frequenc.y domain and time domain approaches have been widely used in the analysis of linear time series models. However. many physical phenomena cannot be adequately represented by linear models; hence the necessity of nonlinear models and higher order spectra. Recently a number of nonlinear models have been proposed. In this monograph we restrict attention to one particular nonlinear model. known as the "bilinear model". The most interesting feature of such a model is that its second order covariance analysis is ve~ similar to that for a linear model. This demonstrates the importance of higher order covariance analysis for nonlinear models. For bilinear models it is also possible to obtain analytic expressions for covariances. spectra. etc. which are often difficult to obtain for other proposed nonlinear models. Estimation of bispectrum and its use in the construction of tests for linearit,y and symmetry are also discussed. All the methods are illustrated with simulated and real data. The first author would like to acknowledge the benefit he received in the preparation of this monograph from delivering a series of lectures on the topic of bilinear models at the University of Bielefeld. Ecole Normale Superieure. University of Paris (South) and the Mathematisch Cen trum. Ams terdam.
Author: D N Shanbhag Publisher: Gulf Professional Publishing ISBN: 9780444500137 Category : Computers Languages : en Pages : 1028
Book Description
This sequel to volume 19 of Handbook on Statistics on Stochastic Processes: Modelling and Simulation is concerned mainly with the theme of reviewing and, in some cases, unifying with new ideas the different lines of research and developments in stochastic processes of applied flavour. This volume consists of 23 chapters addressing various topics in stochastic processes. These include, among others, those on manufacturing systems, random graphs, reliability, epidemic modelling, self-similar processes, empirical processes, time series models, extreme value therapy, applications of Markov chains, modelling with Monte Carlo techniques, and stochastic processes in subjects such as engineering, telecommunications, biology, astronomy and chemistry. particular with modelling, simulation techniques and numerical methods concerned with stochastic processes. The scope of the project involving this volume as well as volume 19 is already clarified in the preface of volume 19. The present volume completes the aim of the project and should serve as an aid to students, teachers, researchers and practitioners interested in applied stochastic processes.
Author: Peter J. Brockwell Publisher: Springer Science & Business Media ISBN: 1441903208 Category : Mathematics Languages : en Pages : 591
Book Description
This edition contains a large number of additions and corrections scattered throughout the text, including the incorporation of a new chapter on state-space models. The companion diskette for the IBM PC has expanded into the software package ITSM: An Interactive Time Series Modelling Package for the PC, which includes a manual and can be ordered from Springer-Verlag. * We are indebted to many readers who have used the book and programs and made suggestions for improvements. Unfortunately there is not enough space to acknowledge all who have contributed in this way; however, special mention must be made of our prize-winning fault-finders, Sid Resnick and F. Pukelsheim. Special mention should also be made of Anthony Brockwell, whose advice and support on computing matters was invaluable in the preparation of the new diskettes. We have been fortunate to work on the new edition in the excellent environments provided by the University of Melbourne and Colorado State University. We thank Duane Boes particularly for his support and encouragement throughout, and the Australian Research Council and National Science Foundation for their support of research related to the new material. We are also indebted to Springer-Verlag for their constant support and assistance in preparing the second edition. Fort Collins, Colorado P. J. BROCKWELL November, 1990 R. A. DAVIS * /TSM: An Interactive Time Series Modelling Package for the PC by P. J. Brockwell and R. A. Davis. ISBN: 0-387-97482-2; 1991.
Author: Susan R. Wilson Publisher: EOLSS Publications ISBN: 1905839367 Category : Mathematics Languages : en Pages : 342
Book Description
Biometrics is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. Biometry is a broad discipline covering all applications of statistics and mathematics to biology. The Theme Biometrics is divided into areas of expertise essential for a proper application of statistical and mathematical methods to contemporary biological problems. These volumes cover four main topics: Data Collection and Analysis, Statistical Methodology, Computation, Biostatistical Methods and Research Design and Selected Topics. These volumes are aimed at the following five major target audiences: University and College students Educators, Professional practitioners, Research personnel and Policy analysts, managers, and decision makers and NGOs.
Author: Howell A M Tong Publisher: World Scientific ISBN: 9814504378 Category : Mathematics Languages : en Pages : 232
Book Description
This volume is the first in the new series Nonlinear Time Series and Chaos. The general aim of the series is to provide a bridge between the two communities by inviting prominent researchers in their respective fields to give a systematic account of their chosen topics, starting at the beginning and ending with the latest state. It is hoped that researchers in both communities will find the topics relevant and thought provoking. In this volume, the first chapter, written by Professor Colleen Cutler, is a comprehensive account of the theory and estimation of fractal dimension, a topic of central importance in dynamical systems, which has recently attracted the attention of the statisticians. As it is natural to study a stochastic dynamical system within the framework of Markov chains, it is therefore relevant to study their limiting behaviour. The second chapter, written by Professor Kung-Sik Chan, reviews some limit theorems of Markov chains and illustrates their relevance to chaos. The next three chapters are concerned with specific models. Briefly, Chapter Three by Professor Peter Lewis and Dr Bonnie Ray and Chapter Four by Professor Peter Brockwell generalise the class of self-exciting threshold autoregressive models in different directions. In Chapter Three, the new and powerful methodology of multivariate adaptive regression splines (MARS) is adapted to time series data. Its versatility is illustrated by reference to the very interesting and complex sea surface temperature data. Chapter Four exploits the greater tractability of continuous-time Markov approach to discrete-time data. The approach is particularly relevant to irregularly sampled data. The concluding chapter, by Professor Pham Dinh Tuan, is likely to be the most definitive account of bilinear models in discrete time to date.
Author: T. Subba Rao Publisher: CRC Press ISBN: 9780412492600 Category : Mathematics Languages : en Pages : 466
Book Description
This volume contains 27 papers, written by time series analysts, dealing with statistical theory, methodology and applications. The emphasis is on the recent developments in the analysis of linear, onlinear (non-Gaussian), stationary and nonstationary time series. The topics include cointegration, estimation and asymptotic theory, Kalman filtering, nonparametric statistical inference, long memory models, nonlinear models, spectral analysis of stationary and nonstationary processes. Quite a number of papers are devoted to modelling and analysis of real time series, and the econometricians, mathematical statisticians, communications engineers and scientists who use time series techniques and Fourier analysis should find the papers in this volume useful.
Author: Peter J. Brockwell Publisher: Springer ISBN: 3319298542 Category : Mathematics Languages : en Pages : 428
Book Description
This book is aimed at the reader who wishes to gain a working knowledge of time series and forecasting methods as applied to economics, engineering and the natural and social sciences. It assumes knowledge only of basic calculus, matrix algebra and elementary statistics. This third edition contains detailed instructions for the use of the professional version of the Windows-based computer package ITSM2000, now available as a free download from the Springer Extras website. The logic and tools of time series model-building are developed in detail. Numerous exercises are included and the software can be used to analyze and forecast data sets of the user's own choosing. The book can also be used in conjunction with other time series packages such as those included in R. The programs in ITSM2000 however are menu-driven and can be used with minimal investment of time in the computational details. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Many additional special topics are also covered. New to this edition: A chapter devoted to Financial Time Series Introductions to Brownian motion, Lévy processes and Itô calculus An expanded section on continuous-time ARMA processes
Author: Sakutaro Yamada Publisher: Springer Science & Business Media ISBN: 1461226449 Category : Mathematics Languages : en Pages : 138
Book Description
In the present work I want to show a mathematical study of the statistical notion of sufficiency mainly for undominated statistical experiments. The famous Burkholder's (1961) and Pitcher's(1957) examples motivated some researchers to develop new theory of sufficiency. Le Cam (1964) is probably the most excellent paper in this field of study. This note also belongs to the same area. Though it is more restrictive than Le Cam's paper(1964), a study which is connected more directly with the classical papers of Halmos and Savage(1949) , and Bahadur(1954) is shown. Namely I want to develop a study based on the notion of pivotal measure which was introduced by Halmos and Savage(1949) . It is great pleasure to have this opportunity to thank Professor H. Heyer and Professor H. Morimoto for their careful reading the manuscript and valuable comments on it. I am also thankful to Professor H. Luschgy and Professor D. Mussmann for thei r proposal of wr i ting "the note". I would like to dedicate this note to the memory of my father Eizo.
Author: Werner Vach Publisher: Springer Science & Business Media ISBN: 1461226503 Category : Mathematics Languages : en Pages : 152
Book Description
In many areas of science a basic task is to assess the influence of several factors on a quantity of interest. If this quantity is binary logistic, regression models provide a powerful tool for this purpose. This monograph presents an account of the use of logistic regression in the case where missing values in the variables prevent the use of standard techniques. Such situations occur frequently across a wide range of statistical applications. The emphasis of this book is on methods related to the classical maximum likelihood principle. The author reviews the essentials of logistic regression and discusses the variety of mechanisms which might cause missing values while the rest of the book covers the methods which may be used to deal with missing values and their effectiveness. Researchers across a range of disciplines and graduate students in statistics and biostatistics will find this a readable account of this.
Author: Jesper Moller Publisher: Springer Science & Business Media ISBN: 146122652X Category : Mathematics Languages : en Pages : 144
Book Description
Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.
Author: T.S. Rao
Author: T.S. Rao
Author: D N Shanbhag
Author: Peter J. Brockwell
Author: Susan R. Wilson
Author: Howell A M Tong
Author: T. Subba Rao
Author: Peter J. Brockwell
Author: Sakutaro Yamada
Author: Werner Vach
Author: Jesper Moller