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Author : Ilʹdar Abdulovich Ibragimov,I︠U︡riĭ Vladimirovich Linnik,I͡Uriĭ Vladimirovich Linnik
Publisher : Unknown
Page : 456 pages
File Size : 54,5 Mb
Release : 1971
Category : Distribution (Probability theory).
ISBN : UCAL:B4405420
Author : Murray Rosenblatt
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251569
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.
Author : M. R. Leadbetter,G. Lindgren,H. Rootzen
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461254492
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Author : Robert Cogburn
Publisher : Unknown
Page : 62 pages
File Size : 41,8 Mb
Release : 1960
Category : Convergence
ISBN : CORNELL:31924001424948
Author : V.V. Petrov
Publisher : Springer Science & Business Media
Page : 360 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642658099
The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity
Author : Murad Taqqu,Eberlein
Publisher : Springer-Verlag
Page : 468 pages
File Size : 47,5 Mb
Release : 2019-06-12
Category : Mathematics
ISBN : 9781461581628
Author : Valentin V. Petrov
Publisher : Unknown
Page : 292 pages
File Size : 46,7 Mb
Release : 1995
Category : Electronic
ISBN : OCLC:1023873453
Author : Wilbur B. Davenport
Publisher : Unknown
Page : 586 pages
File Size : 46,9 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015011136515
Author : Peyton Peebles
Publisher : McGraw-Hill Science/Engineering/Math
Page : 488 pages
File Size : 46,6 Mb
Release : 2001
Category : Mathematics
ISBN : STANFORD:36105028511272
Probability - The Random Variable - Operations on one Random Variable--Expectation - Multiple Random Variables - Operations of Multiple Random Variables - Random Processes-Temporal Characteristics - Random Processes-Spectral Characteristics - Linear Systems with Random Inputs - Optimum Linear Systems - Some Practical Applications of the Theory.
Author : E. Wong
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 41,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475717952
Author : Athanasios Papoulis
Publisher : McGraw-Hill Companies
Page : 604 pages
File Size : 42,9 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015010896226
Author : Herold Dehling,Thomas Mikosch,Michael Sörensen
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200994
Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,
Author : Geoffrey Grimmett,David Stirzaker
Publisher : Oxford University Press
Page : 626 pages
File Size : 44,8 Mb
Release : 2001-05-31
Category : Mathematics
ISBN : 0198572220
This textbook provides a wide-ranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions.
Author : Serguei Y. Novak
Publisher : CRC Press
Page : 402 pages
File Size : 44,5 Mb
Release : 2011-12-20
Category : Mathematics
ISBN : 9781439835746
Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible. Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers: Extremes in samples of random size Methods of estimating extreme quantiles and tail probabilities Self-normalized sums of random variables Measures of market risk Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text. A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.
Author : Valentin Vladimirovich Petrov
Publisher : Unknown
Page : 292 pages
File Size : 53,7 Mb
Release : 1995
Category : Limit theorems (Probability theory)
ISBN : OCLC:1176259470
Limit theorems and probability inequalities for sums of independent random variables are beneficial to those studying probability and statistics. This treatise presents a clear exposition of classical and modern results in the field.
