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Author : Florin Avram
Publisher :
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4.E/5 ( download)
Download or read book Some Limit Theorems for Stationary Sequences with Infinite Or Finite Variance written by Florin Avram and published by . This book was released on 1986 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Armine Bagyan
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (927 download)
Download or read book Central Limit Theorems for Randomly Modulated Sequences of Random Vectors with Resampling and Applications to Statistics written by Armine Bagyan and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In many situations when sequences of random vectors are under consideration, it is of interest to study the asymptotic distribution of their (normalized) sums and to determine the conditions for the limit theorems, such as the Central Limit Theorem (CLT), to hold. In the simplest case when the variables are independent and identically distributed and have finite variance, the CLT is satisfied. Some CLT generalizations with weakened independence assumptions exist as well. For example, the CLT holds for stationary random sequences with strong mixing. However, in many situations when there is dependence, the CLT does not hold.%In particular when we consider stationary sequences of random variables.This happens for stationary random sequences even with the weak mixing condition.In our research we propose a method of random modulation of ergodic stationary random sequences that allows us to prove limit theorems for such sequences without any mixing conditions. These theorems present an opportunity to construct asymptotic confidence intervals for parameters, test parametric and non-parametric hypotheses with the significance level close to the required one and to calculate the approximate power of the test.More general analogs of the CLT are proved and the speed of convergence is estimated for sequences of random vectors in spaces of non-decreasing dimensions.
Author : R. R. Bahadur
Publisher : SIAM
ISBN 13 : 9781611970630
Total Pages : 48 pages
Book Rating : 4.9/5 (76 download)
Download or read book Some Limit Theorems in Statistics written by R. R. Bahadur and published by SIAM. This book was released on 1971-01-01 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of some topics in the theory of large deviations such as moment-generating functions and Chernoff's theorem, and of aspects of estimation and testing in large samples, such as exact slopes of test statistics.
Author : STANFORD UNIV CALIF DEPT OF STATISTICS.
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (123 download)
Download or read book On the Central Limit Theorem for Stationary Processes written by STANFORD UNIV CALIF DEPT OF STATISTICS. and published by . This book was released on 1973 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central limit theorem is given with application to a wide class of processes ((S sub M) = summation from i = 1 to n of (X sub i)) with stationary ergodic increments (X sub i) having zero mean and finite variance and such that lim as N approaches infinity (N sup -1) E (S sup 2, sub n) = (Sigma squared), 0
Author : Michael George Maxwell
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.3/5 (91 download)
Download or read book Local and Global Central Limit Theorems for Stationary Ergodic Sequences written by Michael George Maxwell and published by . This book was released on 1997 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Adler
Publisher : Springer Science & Business Media
ISBN 13 : 9780817639518
Total Pages : 560 pages
Book Rating : 4.6/5 (395 download)
Download or read book A Practical Guide to Heavy Tails written by Robert Adler and published by Springer Science & Business Media. This book was released on 1998-10-26 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Alexander Bulinski
Publisher : World Scientific
ISBN 13 : 9814474576
Total Pages : 447 pages
Book Rating : 4.8/5 (144 download)
Download or read book Limit Theorems For Associated Random Fields And Related Systems written by Alexander Bulinski and published by World Scientific. This book was released on 2007-09-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications.There are 434 items in the bibliography.The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
Author : Michael R. Chernick
Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.F/5 ( download)
Download or read book Mixing Conditions and Limit Theorems for Maxima of Some Stationary Sequences written by Michael R. Chernick and published by . This book was released on 1978 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul Doukhan
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641689
Total Pages : 744 pages
Book Rating : 4.6/5 (416 download)
Download or read book Theory and Applications of Long-Range Dependence written by Paul Doukhan and published by Springer Science & Business Media. This book was released on 2002-12-13 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject. The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, and prediction for long-range dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques." Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, prediction for long-range dependence sequences. The reader is referred to more detailed proofs if already found in the literature. The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a state-of-the art reference or graduate seminar text.
Author : Pál Révész
Publisher : Elsevier Science & Technology
ISBN 13 :
Total Pages : 574 pages
Book Rating : 4.:/5 (318 download)
Download or read book Limit Theorems in Probability and Statistics written by Pál Révész and published by Elsevier Science & Technology. This book was released on 1984 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yu.V. Prokhorov
Publisher : Springer
ISBN 13 : 9783642081705
Total Pages : 273 pages
Book Rating : 4.0/5 (817 download)
Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer. This book was released on 2010-12-01 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.
Author : R. J. Serfling
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (227 download)
Download or read book Central Limit Theorems for Weakly Stationary Sequences written by R. J. Serfling and published by . This book was released on 1966 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of stochastic processes often involves weakly stationary sequences of random variables. The usefulness of central limit theory in inference based upon large samples of independent variables encourages efforts to carry it over to such sequences of dependent variables. The specialization of a theorem of Hoeffding and Robbins to weakly stationary and m-dependent sequences is generalized herein to a wide class of weakly stationary sequences. Various ways of restricting dependence are discussed. Strigent conditions such as strict stationarity and strong mixing are not assumed, so wide applicability is possible. (Author).
Author : Boris Nahapetian
Publisher : Springer
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.3/5 (91 download)
Download or read book Limit Theorems and Some Applications in Statistical Physics written by Boris Nahapetian and published by Springer. This book was released on 1991-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ward Whitt
Publisher : Springer Science & Business Media
ISBN 13 : 0387217487
Total Pages : 616 pages
Book Rating : 4.3/5 (872 download)
Download or read book Stochastic-Process Limits written by Ward Whitt and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
Author : Ernest G. Kimme
Publisher :
ISBN 13 :
Total Pages : 198 pages
Book Rating : 4.3/5 (91 download)
Download or read book Limit Theorems for the Distributions of the Maxima of Partial Sums of Independent Random Variables written by Ernest G. Kimme and published by . This book was released on 1957 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Evarist Giné
Publisher : Cambridge University Press
ISBN 13 : 1009022784
Total Pages : 706 pages
Book Rating : 4.0/5 (9 download)
Download or read book Mathematical Foundations of Infinite-Dimensional Statistical Models written by Evarist Giné and published by Cambridge University Press. This book was released on 2021-03-25 with total page 706 pages. Available in PDF, EPUB and Kindle. Book excerpt: In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.
Author :
Publisher :
ISBN 13 :
Total Pages : 574 pages
Book Rating : 4.3/5 (91 download)
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
