Series Approximation Methods in Statistics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Series Approximation Methods in Statistics PDF full book. Access full book title Series Approximation Methods in Statistics by John Edward Kolassa. Download full books in PDF and EPUB format.
Author: John Edward Kolassa Publisher: Springer Science & Business Media ISBN: 9780387942773 Category : Mathematics Languages : en Pages : 150
Book Description
Asymptotic techniques have long been important in statistical inference; these techniques remain important in the age of fast computing because some exact answers are still either conceptually unavailable or practically out of reach. This book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple, and in a few complicated, settings. Numerical and asymptotic assessments of accuracy are presented. Variants of these expansions, including much of modern likelihood theory, are discussed. Applications to lattice distributions are extensively treated.
Author: John Edward Kolassa Publisher: Springer Science & Business Media ISBN: 9780387942773 Category : Mathematics Languages : en Pages : 150
Book Description
Asymptotic techniques have long been important in statistical inference; these techniques remain important in the age of fast computing because some exact answers are still either conceptually unavailable or practically out of reach. This book presents theoretical results relevant to Edgeworth and saddlepoint expansions to densities and distribution functions. It provides examples of their application in some simple, and in a few complicated, settings. Numerical and asymptotic assessments of accuracy are presented. Variants of these expansions, including much of modern likelihood theory, are discussed. Applications to lattice distributions are extensively treated.
Author: John E. Kolassa Publisher: Springer Science & Business Media ISBN: 1475742754 Category : Mathematics Languages : en Pages : 162
Book Description
This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.
Author: Rolf-Dieter Reiss Publisher: Springer Science & Business Media ISBN: 1461396204 Category : Mathematics Languages : en Pages : 363
Book Description
This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.
Author: Peter McCullagh Publisher: Courier Dover Publications ISBN: 0486832694 Category : Mathematics Languages : en Pages : 308
Book Description
A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.
Author: Byron Ellis Publisher: John Wiley & Sons ISBN: 1118838025 Category : Computers Languages : en Pages : 432
Book Description
Construct a robust end-to-end solution for analyzing and visualizing streaming data Real-time analytics is the hottest topic in data analytics today. In Real-Time Analytics: Techniques to Analyze and Visualize Streaming Data, expert Byron Ellis teaches data analysts technologies to build an effective real-time analytics platform. This platform can then be used to make sense of the constantly changing data that is beginning to outpace traditional batch-based analysis platforms. The author is among a very few leading experts in the field. He has a prestigious background in research, development, analytics, real-time visualization, and Big Data streaming and is uniquely qualified to help you explore this revolutionary field. Moving from a description of the overall analytic architecture of real-time analytics to using specific tools to obtain targeted results, Real-Time Analytics leverages open source and modern commercial tools to construct robust, efficient systems that can provide real-time analysis in a cost-effective manner. The book includes: A deep discussion of streaming data systems and architectures Instructions for analyzing, storing, and delivering streaming data Tips on aggregating data and working with sets Information on data warehousing options and techniques Real-Time Analytics includes in-depth case studies for website analytics, Big Data, visualizing streaming and mobile data, and mining and visualizing operational data flows. The book's "recipe" layout lets readers quickly learn and implement different techniques. All of the code examples presented in the book, along with their related data sets, are available on the companion website.
Author: Armin Iske Publisher: Springer ISBN: 3030052281 Category : Mathematics Languages : en Pages : 358
Book Description
This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.
Author: Louis H.Y. Chen Publisher: Springer Science & Business Media ISBN: 3642150071 Category : Mathematics Languages : en Pages : 408
Book Description
Since its introduction in 1972, Stein’s method has offered a completely novel way of evaluating the quality of normal approximations. Through its characterizing equation approach, it is able to provide approximation error bounds in a wide variety of situations, even in the presence of complicated dependence. Use of the method thus opens the door to the analysis of random phenomena arising in areas including statistics, physics, and molecular biology. Though Stein's method for normal approximation is now mature, the literature has so far lacked a complete self contained treatment. This volume contains thorough coverage of the method’s fundamentals, includes a large number of recent developments in both theory and applications, and will help accelerate the appreciation, understanding, and use of Stein's method by providing the reader with the tools needed to apply it in new situations. It addresses researchers as well as graduate students in Probability, Statistics and Combinatorics.
Author: Harold Cohen Publisher: Springer Science & Business Media ISBN: 1441998365 Category : Mathematics Languages : en Pages : 493
Book Description
This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Author: Rudolf J. Freund Publisher: Elsevier ISBN: 0080498221 Category : Mathematics Languages : en Pages : 694
Book Description
This broad text provides a complete overview of most standard statistical methods, including multiple regression, analysis of variance, experimental design, and sampling techniques. Assuming a background of only two years of high school algebra, this book teaches intelligent data analysis and covers the principles of good data collection. * Provides a complete discussion of analysis of data including estimation, diagnostics, and remedial actions * Examples contain graphical illustration for ease of interpretation * Intended for use with almost any statistical software * Examples are worked to a logical conclusion, including interpretation of results * A complete Instructor's Manual is available to adopters
Author: John Edward Kolassa
Author: John Edward Kolassa
Author: John E. Kolassa
Author: John E. Kolassa
Author: Rolf-Dieter Reiss
Author: Peter McCullagh
Author: Byron Ellis
Author: Armin Iske
Author: Louis H.Y. Chen
Author: Harold Cohen
Author: Rudolf J. Freund