the statistical theory of linear systems

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The Statistical Theory Of Linear Systems

Author : E. J. Hannan
ISBN : 9781611972184
Genre : Business & Economics
File Size : 53. 87 MB
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Originally published: New York: Wiley, c1988.

Developments In Statistics

Author : Paruchuri R. Krishnaiah
ISBN : 9781483264196
Genre : Mathematics
File Size : 71. 22 MB
Format : PDF
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Development in Statistics, Volume 2 is a collection of papers that deals with one- and two- dimensional structures, the statistical theory of linear systems, bispectra, and energy transfer in grid-generated turbulence. Several papers discuss simultaneous test procedures, stochastic Markovian fields, as well as the stopping of invariant sequential probability ratio tests. One paper examines the relationships between excitation and response statistics for one-dimensional structures, and then as extended to two-dimensional structures. The special features issuing from these extensions are related to simple supported rectangular and square plates excited by a stationary random force applied at a single point. Another paper discuses the relationship between the measurable bispectra and the one-dimensional energy transfer terms, and which bispectra will vanish in an isotropic turbulent flow field. One paper reviews simultaneous test procedures, including the evaluation of the probability integrals of multivariates, multivariate gamma distributions, distributions of correlated quadratic forms. Another paper analyzes two concerns regarding the random sample size N, also known as stopping time. These are if N is finite with a probability of one, or the rate that the tail probabilities in the distribution of N go to zero. Mathematicians, statisticians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.

Linear Statistical Models

Author : James H. Stapleton
ISBN : 9780470317761
Genre : Mathematics
File Size : 38. 90 MB
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Linear Statistical Models Developed and refined over a period of twenty years, the material in this book offers an especially lucid presentation of linear statistical models. These models lead to what is usually called "multiple regression" or "analysis of variance" methodology, which, in turn, opens up a wide range of applications to the physical, biological, and social sciences, as well as to business, agriculture, and engineering. Unlike similar books on this topic, Linear Statistical Models emphasizes the geometry of vector spaces because of the intuitive insights this approach brings to an understanding of the theory. While the focus is on theory, examples of applications, using the SAS and S-Plus packages, are included. Prerequisites include some familiarity with linear algebra, and probability and statistics at the postcalculus level. Major topics covered include: * Methods of study of random vectors, including the multivariate normal, chi-square, t and F distributions, central and noncentral * The linear model and the basic theory of regression analysis and the analysis of variance * Multiple regression methods, including transformations, analysis of residuals, and asymptotic theory for regression analysis. Separate sections are devoted to robust methods and to the bootstrap. * Simultaneous confidence intervals: Bonferroni, Scheffe, Tukey, and Bechhofer * Analysis of variance, with two- and three-way analysis of variance * Random component models, nested designs, and balanced incomplete block designs * Analysis of frequency data through log-linear models, with emphasis on vector space viewpoint. This chapter alone is sufficient for a course on the analysis of frequency data.

Statistical Theory Of Communication

Author : S.P. Eugene Xavier
ISBN : 8122411274
Genre :
File Size : 26. 91 MB
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This Book Deals With The Application Of Statistics To Communication Systems And Radar Signal Processing. Information Theory, Coding, Random Processes, Optimum Linear Systems And Estimation Theory Forms The Subject Matter Of This Book. The Subject Treatment Requires A Basic Knowledge Of Probability And Statistics. This Book Is Intended As A Text For A Graduate Level Course On Electronics And Communication Engineering.

A Course In Time Series Analysis

Author : Daniel Peña
ISBN : 9781118031223
Genre : Mathematics
File Size : 37. 85 MB
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New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include: Contributions from eleven of the worldâ??s leading figures in time series Shared balance between theory and application Exercise series sets Many real data examples Consistent style and clear, common notation in all contributions 60 helpful graphs and tables Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Mathematics Of Chance

Author : Jirí Andel
ISBN : 9780470317914
Genre : Mathematics
File Size : 90. 31 MB
Format : PDF
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Mathematics of Chance utilizes simple, real-world problems-some of which have only recently been solved-to explain fundamental probability theorems, methods, and statistical reasoning. Jiri Andel begins with a basic introduction to probability theory and its important points before moving on to more specific sections on vital aspects of probability, using both classic and modern problems. Each chapter begins with easy, realistic examples before covering the general formulations and mathematical treatments used. The reader will find ample use for a chapter devoted to matrix games and problem sets concerning waiting, probability calculations, expectation calculations, and statistical methods. A special chapter utilizes problems that relate to areas of mathematics outside of statistics and considers certain mathematical concepts from a probabilistic point of view. Sections and problems cover topics including: * Random walks * Principle of reflection * Probabilistic aspects of records * Geometric distribution * Optimization * The LAD method, and more Knowledge of the basic elements of calculus will be sufficient in understanding most of the material presented here, and little knowledge of pure statistics is required. Jiri Andel has produced a compact reference for applied statisticians working in industry and the social and technical sciences, and a book that suits the needs of students seeking a fundamental understanding of probability theory.

The Theory Of Measures And Integration

Author : Eric M. Vestrup
ISBN : 9780470317952
Genre : Mathematics
File Size : 37. 77 MB
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An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry. Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include: * Measurable Functions * The Lp Spaces * The Radon-Nikodym Theorem * Products of Two Measure Spaces * Arbitrary Products of Measure Spaces Sections conclude with exercises that range in difficulty between easy "finger exercises"and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics. In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics.

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