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.

Statistics has been a main tool in almost every field of activity and an essential part of applied scientific work, supporting conclusions and offering insights into new uses for established methodologies, thus making it a valuable resource in looking for faceless facts. Model construction describing populations or phenomena subject to randomness use a wide range of methods. Data collection provides the basis for modelling and assumption verification. Modelling must be conducted using suitable techniques that give researchers the means to search for hidden facts or behaviours. This may be addressed by fitting pre-defined shapes and distributions to the data or by allowing the data to reveal its intrinsic properties by using nonparametric methods. This volume contains a selection of contributions presented at the XVIII Annual Congress of the Portuguese Statistical Society.

Statistics has been a main tool in almost every field of activity and an essential part of applied scientific work, supporting conclusions and offering insights into new uses for established methodologies, thus making it a valuable resource in looking for faceless facts. Model construction describing populations or phenomena subject to randomness use a wide range of methods. Data collection provides the basis for modelling and assumption verification. Modelling must be conducted using suitable techniques that give researchers the means to search for hidden facts or behaviours. This may be addressed by fitting pre-defined shapes and distributions to the data or by allowing the data to reveal its intrinsic properties by using nonparametric methods. This volume contains a selection of contributions presented at the XVIII Annual Congress of the Portuguese Statistical Society.

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.