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Asymptotics for Associated Random Variables

  • Paulo Eduardo Oliveira

Table of contents

  1. Front Matter
    Pages I-X
  2. Paulo Eduardo Oliveira
    Pages 1-33
  3. Paulo Eduardo Oliveira
    Pages 35-66
  4. Paulo Eduardo Oliveira
    Pages 67-100
  5. Paulo Eduardo Oliveira
    Pages 101-127
  6. Paulo Eduardo Oliveira
    Pages 129-170
  7. Back Matter
    Pages 171-194

About this book

Introduction

The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting the theory in a unified way, explaining relations and implications of the results. It will present basic definitions and characterizations, followed by a collection of relevant inequalities. These are then applied to characterize almost sure and weak convergence of sequences of associated variables. It will also cover applications of positive dependence to the characterization of asymptotic results in nonparametric statistics. The book is directed towards researchers in probability and statistics, with particular emphasis on people interested in nonparametric methods. It will also be of interest to graduate students in those areas. The book could also be used as a reference on association in a course covering dependent variables and their asymptotics.
As prerequisite, readers should have knowledge of basic probability on the reals and on metric spaces. Some acquaintance with the asymptotics of random functions, such us empirical processes and partial sums processes, is useful but not essential.

Keywords

association inequalities limit theorems nonparametric estimations

Authors and affiliations

  • Paulo Eduardo Oliveira
    • 1
  1. 1.Department of MathematicsUniversity of CoimbraCoimbraPortugal

Bibliographic information

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