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Associated Sequences, Demimartingales and Nonparametric Inference
This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. One of the basic aims of theory of probability and statistics is to build stochastic models which explain the phenomenon under investigation and explore the dependence among various covariates which influence this phenomenon. Classic examples are the concepts of Markov dependence or of mixing for random processes. Esary, Proschan and Walkup introduced the concept of association for random variables, and Newman and Wright studied properties of processes termed as demimartingales. It can be shown that the partial sums of mean zero associated random variables form a demimartingale. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to problems in nonparametric statistical inference for such processes are investigated in the last three chapters. This book will appeal to graduate students and researchers interested in probabilistic aspects of various types of stochastic processes and their applications in reliability theory, statistical mechanics, percolation theory and other areas.
Preface -- Associated Random Variables and Related Concepts -- Demimartingales -- N-Demimartingales -- Conditional Demimartingales -- Multidimensionally Indexed Demimartingales and Continuous Parameter Demimartingales -- Limit Theorems for Associated Random Variables -- Nonparametric Estimation for Associated Sequences -- Nonparametric Tests for Associated Sequences -- Nonparametric Tests for Change in Marginal Density Function for Associated Sequences -- References -- Index.
Probability Theory and Stochastic Processes