Titlebook: Asymptotics for Associated Random Variables; Paulo Eduardo Oliveira Book 2012 Springer-Verlag Berlin Heidelberg 2012 association.inequalit

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ADORE

or associated samples.Uses a elementary approach while inclu.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 communit

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Gordian R?ttich,Kim Clark,Evi Hartmannults, we will find characterizations of convergence rates with respect to the usual supnorm metric between distribution functions. A few applications to statistical estimation problems will be addressed in the final section of this chapter, as done in the previous one.

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Positive Dependence,, highlighting the connections with the order structure of the underlying space. The chapter is concluded with a reference to other types of positive dependence and their relations. A brief discussion on negative dependence notions concludes the chapter.

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Book 20121966 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 es

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Inequalities,ove convergence results. Sect.?. shows that at least the convergence in distribution is concerned with the covariance structure that completely describes the behaviour of associated variables. This chapter is a fundamental one for the remaining text.

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Almost Sure Convergence,ery explored theme under association. Here the assumptions on the decay rate of the covariances are much stronger, a behaviour as found for some other dependence structures. The approach and techniques used in this chapter are adapted in the final section to prove almost sure consistency results for