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Boundary Crossing Probabilities And Statistical Applications
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Book Synopsis Boundary Crossing Probabilities and Statistical Applications by : STANFORD UNIV CA DEPT OF STATISTICS.
Download or read book Boundary Crossing Probabilities and Statistical Applications written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1985 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys recent results involving boundary crossing probabilities and related statistical applications. The first part is concerned with problems of sequential analysis, especially repeated significance tests and their application to sequential clinical trials involving survival data. The second part develops the probability theory motivated by the problems of Part 1. A method for computing first passage distributions of Brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries. The third part is concerned with fixed sample statistical problems, especially change-point problems, which involve boundary crossing probabilities. Examples are given of problems for which methods of Part 2 appear adequate and of problems which require new methods.
Book Synopsis Saddlepoint Approximations and Boundary Crossing Probabilities for Random Fields and Their Applications by : T. L. Lai
Download or read book Saddlepoint Approximations and Boundary Crossing Probabilities for Random Fields and Their Applications written by T. L. Lai and published by . This book was released on 2005 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Sample Path Analysis and Distributions of Boundary Crossing Times by : Shelemyahu Zacks
Download or read book Sample Path Analysis and Distributions of Boundary Crossing Times written by Shelemyahu Zacks and published by Springer. This book was released on 2017-10-12 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is focused on the derivations of exact distributions of first boundary crossing times of Poisson processes, compound Poisson processes, and more general renewal processes. The content is limited to the distributions of first boundary crossing times and their applications to various stochastic models. This book provides the theory and techniques for exact computations of distributions and moments of level crossing times. In addition, these techniques could replace simulations in many cases, thus providing more insight about the phenomenona studied. This book takes a general approach for studying telegraph processes and is based on nearly thirty published papers by the author and collaborators over the past twenty five years. No prior knowledge of advanced probability is required, making the book widely available to students and researchers in applied probability, operations research, applied physics, and applied mathematics.
Book Synopsis Conditional Boundary Crossing Probabilities with Applications to Change-point Problems by : STANFORD UNIV CA DEPT OF STATISTICS.
Download or read book Conditional Boundary Crossing Probabilities with Applications to Change-point Problems written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1986 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: For normal random walks S sub 1, S sub 2 ..., formed from independent, identically distributed random variables X sub 1, X sub 2 ..., we determine the asymptotic behavior under regularity conditions of P(S sdub n> mg(n/m) for some n
Book Synopsis Self-Normalized Processes by : Victor H. Peña
Download or read book Self-Normalized Processes written by Victor H. Peña and published by Springer Science & Business Media. This book was released on 2008-12-25 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization.
Book Synopsis Boundary Crossing Probabilities for the Kolmogorov-Smirnov Statistics by : Richard Melvin Stanley
Download or read book Boundary Crossing Probabilities for the Kolmogorov-Smirnov Statistics written by Richard Melvin Stanley and published by . This book was released on 1970 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Boundary Crossing of Brownian Motion by : Hans R. Lerche
Download or read book Boundary Crossing of Brownian Motion written by Hans R. Lerche and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser ved in practice.
Book Synopsis Boundary Crossing Probabilities for U-statistics by : Rasul A. Khan
Download or read book Boundary Crossing Probabilities for U-statistics written by Rasul A. Khan and published by . This book was released on 1971 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let the set (U sub n, n> or = r) be a sequence of U-statistics with mean theta. The author computes upper bounds on the probabilities P(U sub n - theta> or = a sub n for some n> or = m) and P(/U sub n - theta /> or = a sub n for some n> or = m) for certain for certain boundary sequences including a sub n = O(square root (2 loglog n/n)). An invariance theorem is also deduced. (Author).
Book Synopsis Boundary Crossing Probabilities for Diffusion Processes and Related Problems by : Andrew Nicholas Downes
Download or read book Boundary Crossing Probabilities for Diffusion Processes and Related Problems written by Andrew Nicholas Downes and published by . This book was released on 2008 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Large Deviations for Boundary Crossing Probabilities by : STANFORD UNIV CA DEPT OF STATISTICS.
Download or read book Large Deviations for Boundary Crossing Probabilities written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1981 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: For random walsk s sub n, n=1,2, ... whose distribution can be imbedded in an exponential family, a method is described for determining the asymptotic behavior as m goes to infinity of P(s sub n> m c(n/m) for some n
Book Synopsis Probability and Statistical Models with Applications by : CH. A. Charalambides
Download or read book Probability and Statistical Models with Applications written by CH. A. Charalambides and published by CRC Press. This book was released on 2000-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili
Book Synopsis Sequential Analysis by : David Siegmund
Download or read book Sequential Analysis written by David Siegmund and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modern theory of Sequential Analysis came into existence simultaneously in the United States and Great Britain in response to demands for more efficient sampling inspection procedures during World War II. The develop ments were admirably summarized by their principal architect, A. Wald, in his book Sequential Analysis (1947). In spite of the extraordinary accomplishments of this period, there remained some dissatisfaction with the sequential probability ratio test and Wald's analysis of it. (i) The open-ended continuation region with the concomitant possibility of taking an arbitrarily large number of observations seems intol erable in practice. (ii) Wald's elegant approximations based on "neglecting the excess" of the log likelihood ratio over the stopping boundaries are not especially accurate and do not allow one to study the effect oftaking observa tions in groups rather than one at a time. (iii) The beautiful optimality property of the sequential probability ratio test applies only to the artificial problem of testing a simple hypothesis against a simple alternative. In response to these issues and to new motivation from the direction of controlled clinical trials numerous modifications of the sequential probability ratio test were proposed and their properties studied-often by simulation or lengthy numerical computation. (A notable exception is Anderson, 1960; see III.7.) In the past decade it has become possible to give a more complete theoretical analysis of many of the proposals and hence to understand them better.
Book Synopsis Problems in Boundary Crossing for Random Walks by : Michael L. Hogan
Download or read book Problems in Boundary Crossing for Random Walks written by Michael L. Hogan and published by . This book was released on 1984 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scan Statistics written by Joseph Glaz and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many statistical applications, scientists have to analyze the occurrence of observed clusters of events in time or space. Scientists are especially interested in determining whether an observed cluster of events has occurred by chance if it is assumed that the events are distributed independently and uniformly over time or space. Scan statistics have relevant applications in many areas of science and technology including geology, geography, medicine, minefield detection, molecular biology, photography, quality control and reliability theory and radio-optics.
Book Synopsis Boundary crossing probabilities of some random fields related to likelihood ratio tests for epidemic alternatives by : Qiwei Yao
Download or read book Boundary crossing probabilities of some random fields related to likelihood ratio tests for epidemic alternatives written by Qiwei Yao and published by . This book was released on 1991 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Lower Bound for Boundary Crossing Probabilities of Brownian Bridge by : Wolfgang Bischoff
Download or read book A Lower Bound for Boundary Crossing Probabilities of Brownian Bridge written by Wolfgang Bischoff and published by . This book was released on 2018 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Time Series Analysis and Applications to Geophysical Systems by : David Brillinger
Download or read book Time Series Analysis and Applications to Geophysical Systems written by David Brillinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of a two volume set based on a recent IMA program of the same name. The goal of the program and these books is to develop a community of statistical and other scientists kept up-to-date on developments in this quickly evolving and interdisciplinary field. Consequently, these books present recent material by distinguished researchers. Topics discussed in Part I include nonlinear and non- Gaussian models and processes (higher order moments and spectra, nonlinear systems, applications in astronomy, geophysics, engineering, and simulation) and the interaction of time series analysis and statistics (information model identification, categorical valued time series, nonparametric and semiparametric methods). Self-similar processes and long-range dependence (time series with long memory, fractals, 1/f noise, stable noise) and time series research common to engineers and economists (modeling of multivariate and possibly non-stationary time series, state space and adaptive methods) are discussed in Part II.
