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.

Asymptotics for Associated Random Variables. Authors: Oliveira, Paulo Eduardo.

Asymptotics for Associated Random Variables. Paulo Eduardo Aragão Aleixo e Neves de Oliveira is a member of the Centre for Mathematics at the University of Coimbra, where he studied mathematics and received his . c. in mathematics in 1984. He was awarded a P. in applied mathematics from the University of Lille I, France, in 1991. Since then he has held several academic positions at the University of Coimbra and has been a full professor since 2004.

Paulo Eduardo Oliveira (auth. 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.

by Paulo Eduardo Oliveira.

from book Asymptotics for Associated Random Variables (p. 5-66). Paulo Eduardo Oliveira. Chapter · January 2012 with 9 Reads. Cite this publication. University of Coimbra. We prove an exponential inequality for positively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. The proof uses a truncation technique together with a block decomposition of the sums to allow an approximation to independence.

The book concerns the notion of association in probability and statistics. Books related to Asymptotics for Associated Random Variables. Theory of Games and Statistical Decisions.

Oliveira, Paulo Eduardo Verfasser (DE-588)1019385510. Download DOC book format. Publication, Distribution, et. Berlin.

Автор: Paulo Eduardo Oliveira Название: Asymptotics for Associated Random . The book could also be used as a reference on association in a course covering dependent variables and their asymptotics.

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.

Oliveira, P. E. (2012), Asymptotics for Associated Random Variables, Springer. Petrov, V. V. (1995), Limit Theorems of Probability Theory, Oxford University Press. Sen, P. Singer, J. Pedroso de Lima, A. (2009), From Finite Sample to Asymptotic Methods in Statistics, Cambridge University Press. Shiryaev, A. Spokoiny, V. G. (2000), Statistical Experiments and Decisions: Asymptotic theory, World Scientific. Small, C. (2010), Expansions and Asymptotics for Statistics, Chapman & Hall. van der Vaart, A. W. (1998), Asymptotic Statistics, Cambridge University Press.