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Large Deviations For The Maxima Of Some Random Fields
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Book Synopsis Large Deviations for the Maxima of Some Random Fields by : STANFORD UNIV CA DEPT OF STATISTICS.
Download or read book Large Deviations for the Maxima of Some Random Fields written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1985 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several statistical problems which involve the distribution of the maximum of Gaussian random fields are described. Specific examples are the pinned Brownian sheet and a Brownian bridge with 'reflection', which arises in certain change point problems. In these concrete cases the method of Pickands (1969, Trans. Amer. Math. Soc.) is adapted to give large deviation probabilities for the maximum, both for continuous and for discrete indexing sets. A different method is used to give a second order correction for the reflected Brownian bridge and hence for reflected Brownian motion. The numerical accuracy of the approximations is studied via simulation.
Book Synopsis Approximate Tail Probabilities for the Maxima of Some Random Fields by : STANFORD UNIV CA DEPT OF STATISTICS.
Download or read book Approximate Tail Probabilities for the Maxima of Some Random Fields written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1986 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hogan and Siegmund (1986) adapt the method developed by Pickands (1969), Qualls and Watanabe (1973), and Bickel and Rosenblatt (1973) to obtain explicit large deviation approximations for the maxima of several Gaussian random fields arising in statistics. Using a special argument for one particular case, they suggest a heuristic second order approximation for that case; and they show by a Monte Carlo experiment that the second order approximation frequently gives considerably better numerical results. The purpose of this paper is to show that the method developed by Woodroofe (1976,1982) for problems in one dimensional time can be adapted to study maxima of random fields. Overall it involves simpler computations than the previous method and consequently seems potentially capable of delivering a genuine second order approximation should one seem desirable.
Book Synopsis Random Fields and Geometry by : R. J. Adler
Download or read book Random Fields and Geometry written by R. J. Adler and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.
Book Synopsis Selected Works of Murray Rosenblatt by : Richard A. Davis
Download or read book Selected Works of Murray Rosenblatt written by Richard A. Davis and published by Springer Science & Business Media. This book was released on 2011-05-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. Among his many contributions, Rosenblatt conducted seminal work on density estimation, central limit theorems under strong mixing conditions, spectral domain methodology, long memory processes and Markov processes. He has published over 130 papers and 5 books, many as relevant today as when they first appeared decades ago. Murray Rosenblatt was one of the founding members of the Department of Mathematics at the University of California at San Diego (UCSD) and served as advisor to over twenty PhD students. He maintains a close association with UCSD in his role as Professor Emeritus. This volume is a celebration of Murray Rosenblatt's stellar research career that spans over six decades, and includes some of his most interesting and influential papers. Several leading experts provide commentary and reflections on various directions of Murray's research portfolio.
Book Synopsis Extremes in Random Fields by : Benjamin Yakir
Download or read book Extremes in Random Fields written by Benjamin Yakir and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a useful new technique for analyzing the extreme-value behaviour of random fields Modern science typically involves the analysis of increasingly complex data. The extreme values that emerge in the statistical analysis of complex data are often of particular interest. This book focuses on the analytical approximations of the statistical significance of extreme values. Several relatively complex applications of the technique to problems that emerge in practical situations are presented. All the examples are difficult to analyze using classical methods, and as a result, the author presents a novel technique, designed to be more accessible to the user. Extreme value analysis is widely applied in areas such as operational research, bioinformatics, computer science, finance and many other disciplines. This book will be useful for scientists, engineers and advanced graduate students who need to develop their own statistical tools for the analysis of their data. Whilst this book may not provide the reader with the specific answer it will inspire them to rethink their problem in the context of random fields, apply the method, and produce a solution.
Book Synopsis Probability Theory by : Louis H. Y. Chen
Download or read book Probability Theory written by Louis H. Y. Chen and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-03-30 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1985 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weak Convergence and Empirical Processes by : AW van der Vaart
Download or read book Weak Convergence and Empirical Processes written by AW van der Vaart and published by Springer Science & Business Media. This book was released on 1996-03-14 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.
Book Synopsis An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes by : Robert J. Adler
Download or read book An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes written by Robert J. Adler and published by IMS. This book was released on 1990 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Geometry of Random Fields by : Robert J. Adler
Download or read book The Geometry of Random Fields written by Robert J. Adler and published by SIAM. This book was released on 1981-01-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and nonsmooth random fields; closed form expressions for the various geometric characteristics of the excursion sets of smooth, stationary, Gaussian random fields over N-dimensional rectangles; descriptions of the local behavior of random fields in the neighborhoods of high maxima; and a treatment of the Markov property for Gaussian fields. Audience: researchers in probability and statistics, with no prior knowledge of geometry required. Since the book was originally published it has become a standard reference in areas of physical oceanography, cosmology, and neuroimaging. It is written at a level accessible to nonspecialists, including advanced undergraduates and early graduate students.
Book Synopsis Nonparametric Methods in Change Point Problems by : E. Brodsky
Download or read book Nonparametric Methods in Change Point Problems written by E. Brodsky and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The explosive development of information science and technology puts in new problems involving statistical data analysis. These problems result from higher re quirements concerning the reliability of statistical decisions, the accuracy of math ematical models and the quality of control in complex systems. A new aspect of statistical analysis has emerged, closely connected with one of the basic questions of cynergetics: how to "compress" large volumes of experimental data in order to extract the most valuable information from data observed. De tection of large "homogeneous" segments of data enables one to identify "hidden" regularities in an object's behavior, to create mathematical models for each seg ment of homogeneity, to choose an appropriate control, etc. Statistical methods dealing with the detection of changes in the characteristics of random processes can be of great use in all these problems. These methods have accompanied the rapid growth in data beginning from the middle of our century. According to a tradition of more than thirty years, we call this sphere of statistical analysis the "theory of change-point detection. " During the last fifteen years, we have witnessed many exciting developments in the theory of change-point detection. New promising directions of research have emerged, and traditional trends have flourished anew. Despite this, most of the results are widely scattered in the literature and few monographs exist. A real need has arisen for up-to-date books which present an account of important current research trends, one of which is the theory of non parametric change--point detection.
Book Synopsis Weak Convergence and Empirical Processes by : A. W. van der Vaart
Download or read book Weak Convergence and Empirical Processes written by A. W. van der Vaart and published by Springer Nature. This book was released on 2023-07-11 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M− and Z−estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with “problems and complements.” Some of these are exercises to help the reader’s understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations of suprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.
Book Synopsis Large Deviations by : S. R. S. Varadhan
Download or read book Large Deviations written by S. R. S. Varadhan and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.
Book Synopsis Probability Approximations via the Poisson Clumping Heuristic by : David Aldous
Download or read book Probability Approximations via the Poisson Clumping Heuristic written by David Aldous and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i. i. d. from a finite alphabet, how long is the longest consecutive (resp. non-consecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a high-dimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i. i. d. sample from a 2-dimensional rotationally-invariant distribution, what is the maximum over all half-spaces of the deviation between the empirical and true distributions? These questions cover a wide cross-section of theoretical and applied probability. The common theme is that they all deal with maxima or min ima, in some sense.
Book Synopsis Maxima of Gaussian Random Fields and Moderate Deviation Approximations to Boundary Crossing Probabilities of Sums of Random Variables with Multidimensional Indices by : Hock Peng Chan
Download or read book Maxima of Gaussian Random Fields and Moderate Deviation Approximations to Boundary Crossing Probabilities of Sums of Random Variables with Multidimensional Indices written by Hock Peng Chan and published by . This book was released on 2003 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Analysis of Random Walks by : A. A. Borovkov
Download or read book Asymptotic Analysis of Random Walks written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Download or read book Scan Statistics written by Joseph Glaz and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scan statistics is currently one of the most active and important areas of research in applied probability and statistics, having applications to a wide variety of fields: archaeology, astronomy, bioinformatics, biosurveillance, molecular biology, genetics, computer science, electrical engineering, geography, material sciences, physics, reconnaissance, reliability and quality control, telecommunication, and epidemiology. Filling a gap in the literature, this self-contained volume brings together a collection of selected chapters illustrating the depth and diversity of theory, methods and applications in the area of scan statistics.
