An Asymptotic Theory for Empirical Reliability and Concentration Processes

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.

An Asymptotic Theory for Empirical Reliability and Concentration Processes

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 Methods in Probability and Statistics

Csörgó, M., Csörgó, S. and Horváth, L. (1986) An Asymptotic Theory for Empirical Reliability and Concentration Processes. Lecture Notes in Statistics 33. Springer-Verlag, Berlin. Csörgó, M., Csörgó, S., Horváth, L. and Mason, ...

Asymptotic Methods in Probability and Statistics

One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97. This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.

Asymptotic Laws and Methods in Stochastics

[A3] M. Csörg ̋o, S. Csörg ̋o and L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. Lecture Notes in Statistics, 33, Springer-Verlag, Berlin, Heidelberg 1986 (171 pages).

Asymptotic Laws and Methods in Stochastics

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.

Empirical Processes with Applications to Statistics

“Asymptotic normality and efficiency of certain nonparametric test statistics,” Ann. Math. Statist., 29, 972–994. CsóRG6, M., CsöRGó, S. AND HoRVATH, L. (1986). An Asymptotic Theory for Empirical Reliability and Concentration Processes, ...

Empirical Processes with Applications to Statistics

Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables. It also includes applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods, and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition.

Branching Processes

13: J. Pfanzagl (with the assistance of W. Wefelmeyer), Contributions to a General Asymptotic Statistical Theory. ... 33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes v, ...

Branching Processes

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

33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes, v, 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data. x,216 pages, 1985.

Random Sums and Branching Stochastic Processes

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.

Nonparametric Statistics for Stochastic Processes

Vol. 33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. v, 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data. x, 216 pages, 1985.

Nonparametric Statistics for Stochastic Processes

This book provides a mathematically rigorous treatment of the theory of nonparametric estimation and prediction for stochastic processes. It discusses discrete time and continuous time, and the emphasis is on the kernel methods. Several new results are presented concerning optimal and superoptimal convergence rates. How to implement the method is discussed in detail and several numerical results are presented. This book will be of interest to specialists in mathematical statistics and to those who wish to apply these methods to practical problems involving time series analysis.

Quantile Processes with Statistical Applications

D. CHIBISOV (1964), Some theorems on the limiting behaviour of empirical distribution functions, ... M. CSORGO, S. CSORGO, L. HORVATH and D. M. MASON (1983), An asymptotic theory for empirical reliability and concentration processes, ...

Quantile Processes with Statistical Applications

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

Csörgö, M., Csörgö, S. and Horváth, L. (1986). An Asymptotic Theory for Empirical Reliability and Concentration Processes. Springer, Berlin. Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics. Wiley, New York.

Multivariate Statistics and Matrices in Statistics


Higher Order Asymptotic Theory for Time Series Analysis

VI, 178 pages, 1985. Vol. 33: M. Csörgö, S. Csörgö, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. V. 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data.

Higher Order Asymptotic Theory for Time Series Analysis

The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.

Asymptotic Methods in Stochastics

An Asymptotic Theory for Empirical Reliability and Concentration Processes . Springer - Verlag , Berlin . [ 9 ] Csörgő , M. , Csörgő , S. and Horváth , L. ( 1987 ) . Estimation of total time on test transforms and Lorenz curves under ...

Asymptotic Methods in Stochastics


Asymptotic Statistics

REFERENCES [BE) R. Beran: Asymptotically efficient adaptive rank estimates in location models. Ann. Stat. ... [CCH] M. Csörgö, S. Csörgö; L. Horvath: An asymptotic theory of empirical reliability and concentration processes. Lect.

Asymptotic Statistics

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)

Advances in Statistical Models for Data Analysis

In particular, Proposition 3 shows that conditionally ony N the estimator OQH .p/ D OF1H.p/ is asymptotically ... Csörg ̋o, M., Csörg ̋o, S., Horváth, L.: An Asymptotic Theory for Empirical Reliability and Concentration Processes.

Advances in Statistical Models for Data Analysis

This edited volume focuses on recent research results in classification, multivariate statistics and machine learning and highlights advances in statistical models for data analysis. The volume provides both methodological developments and contributions to a wide range of application areas such as economics, marketing, education, social sciences and environment. The papers in this volume were first presented at the 9th biannual meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, held in September 2013 at the University of Modena and Reggio Emilia, Italy.

Robust Statistics Data Analysis and Computer Intensive Methods

33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. v., 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data. x,216 pages, 1985. Vol.

Robust Statistics  Data Analysis  and Computer Intensive Methods

To celebrate Peter Huber's 60th birthday in 1994, our university had invited for a festive occasion in the afternoon of Thursday, June 9. The invitation to honour this outstanding personality was followed by about fifty colleagues and former students from, mainly, allover the world. Others, who could not attend, sent their congratulations by mail and e-mail (P. Bickel:" ... It's hard to imagine that Peter turned 60 ... "). After a welcome address by Adalbert Kerber (dean), the following lectures were delivered. Volker Strassen (Konstanz): Almost Sure Primes and Cryptography -an Introduction Frank Hampel (Zurich): On the Philosophical Foundations of Statistics 1 Andreas Buja (Murray Hill): Projections and Sections High-Dimensional Graphics for Data Analysis. The distinguished speakers lauded Peter Huber a hard and fair mathematician, a cooperative and stimulating colleague, and an inspiring and helpful teacher. The Festkolloquium was surrounded with a musical program by the Univer 2 sity's Brass Ensemble. The subsequent Workshop "Robust Statistics, Data Analysis and Computer Intensive Methods" in Schloss Thurnau, Friday until Sunday, June 9-12, was organized about the areas in statistics that Peter Huber himself has markedly shaped. In the time since the conference, most of the contributions could be edited for this volume-a late birthday present-that may give a new impetus to further research in these fields.

Stochastic Visibility in Random Fields

33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. v., 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data. x, 216 pages, 1985.

Stochastic Visibility in Random Fields

The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding of this research by the US Army. Research contracts were first administered through the Office of Naval Research, and subsequently by the Army Research Office. We are most grateful to all involved for this support and encouragement. In 1986 I administered a three-day workshop on problem solving in the area of sto chastic visibility. This workshop was held at the White Sands Missile Range facility. A set of notes with some software were written for this workshop. This workshop led to the incorporation of some of the methods discussed in the present book into the Army simulation package CASTFOREM. Several people encouraged me to extend those notes and write the present monograph on the level of those notes, so that the material will be more widely available for applications.

Stochastic Ordering and Dependence in Applied Probability

33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. v., 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data. x, 216 pages, 1985.

Stochastic Ordering and Dependence in Applied Probability

This book is an introductionary course in stochastic ordering and dependence in the field of applied probability for readers with some background in mathematics. It is based on lectures and senlinars I have been giving for students at Mathematical Institute of Wroclaw University, and on a graduate course a.t Industrial Engineering Department of Texas A&M University, College Station, and addressed to a reader willing to use for example Lebesgue measure, conditional expectations with respect to sigma fields, martingales, or compensators as a common language in this field. In Chapter 1 a selection of one dimensional orderings is presented together with applications in the theory of queues, some parts of this selection are based on the recent literature (not older than five years). In Chapter 2 the material is centered around the strong stochastic ordering in many dimen sional spaces and functional spaces. Necessary facts about conditioning, Markov processes an"d point processes are introduced together with some classical results such as the product formula and Poissonian departure theorem for Jackson networks, or monotonicity results for some re newal processes, then results on stochastic ordering of networks, re~~ment policies and single server queues connected with Markov renewal processes are given. Chapter 3 is devoted to dependence and relations between dependence and ordering, exem plified by results on queueing networks and point processes among others.

Exploring Stochastic Laws

Weighted empirical and quantile processes. Ann. Probab. 14, 31–85. Csörgö, M., Csörgö, S. and Horváth, L. (1986). An Asymptotic Theory for Empirical Reliability and Concentration Processes. Lecture Notes in Statistics 33.

Exploring Stochastic Laws


Statistical Disclosure Control in Practice

Vol. 33: M. Csörgo, S. Csörgo, L. Horváth, An Asymptotic Theory for Empirical Reliability and Concentration Processes. v., 171 pages, 1986. Vol. 34: D.E. Critchlow, Metric Methods for Analyzing Partially Ranked Data. x, 216 pages, 1985.

Statistical Disclosure Control in Practice

The aim of this book is to discuss various aspects associated with disseminating personal or business data collected in censuses or surveys or copied from administrative sources. The problem is to present the data in such a form that they are useful for statistical research and to provide sufficient protection for the individuals or businesses to whom the data refer. The major part of this book is concerned with how to define the disclosure problem and how to deal with it in practical circumstances.