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An Asymptotic Theory for Empirical Reliability and Concentration Processes

An Asymptotic Theory for Empirical Reliability and Concentration Processes
Author: Miklos Csörgö
Publisher: Springer Science & Business Media
Total Pages: 177
Release: 2013-03-14
Genre: Mathematics
ISBN: 1461564204

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Mik16s Cs6rgO and David M. Mason initiated their collaboration on the topics of this book while attending the CBMS-NSF Regional Confer ence at Texas A & M University in 1981. Independently of them, Sandor Cs6rgO and Lajos Horv~th have begun their work on this subject at Szeged University. The idea of writing a monograph together was born when the four of us met in the Conference on Limit Theorems in Probability and Statistics, Veszpr~m 1982. This collaboration resulted in No. 2 of Technical Report Series of the Laboratory for Research in Statistics and Probability of Carleton University and University of Ottawa, 1983. Afterwards David M. Mason has decided to withdraw from this project. The authors wish to thank him for his contributions. In particular, he has called our attention to the reverse martingale property of the empirical process together with the associated Birnbaum-Marshall inequality (cf.,the proofs of Lemmas 2.4 and 3.2) and to the Hardy inequality (cf. the proof of part (iv) of Theorem 4.1). These and several other related remarks helped us push down the 2 moment condition to EX


Asymptotic Laws and Methods in Stochastics

Asymptotic Laws and Methods in Stochastics
Author: Donald Dawson
Publisher: Springer
Total Pages: 401
Release: 2015-11-12
Genre: Mathematics
ISBN: 1493930761

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This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.


Quantile Processes with Statistical Applications

Quantile Processes with Statistical Applications
Author: Miklos Csorgo
Publisher: SIAM
Total Pages: 169
Release: 1983-01-01
Genre: Distribution (Probability theory)
ISBN: 9781611970289

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Provides a comprehensive theory of the approximations of quantile processes in light of recent advances, as well as some of their statistical applications.


Multivariate Statistics and Matrices in Statistics

Multivariate Statistics and Matrices in Statistics
Author: E. M. Tiit
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 352
Release: 2020-05-18
Genre: Mathematics
ISBN: 3112314212

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No detailed description available for "Multivariate Statistics and Matrices in Statistics".


Branching Processes

Branching Processes
Author: C.C. Heyde
Publisher: Springer Science & Business Media
Total Pages: 189
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461225582

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This volume presents the edited proceedings of the First World Congress on Branching Processes. The contributions present new research and surveys of the current research activity in this field. As a result, all those undertaking research in the subject will find this a timely and high-quality volume to have on their shelves.


Random Sums and Branching Stochastic Processes

Random Sums and Branching Stochastic Processes
Author: Ibrahim Rahimov
Publisher: Springer Science & Business Media
Total Pages: 212
Release: 1995-01-06
Genre: Mathematics
ISBN: 9780387944463

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The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.


Asymptotic Statistics

Asymptotic Statistics
Author: Manfred Denker
Publisher: Birkhäuser
Total Pages: 121
Release: 2012-12-06
Genre: Science
ISBN: 3034892543

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These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 {sect}1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx)