B. L. S. Prakasa Rao

Associated Sequences, Demimartingales and Nonparametric Inference (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 272
• Erscheinungstermin: 4. November 2011
• Englisch
• ISBN-13: 9783034802406
• Artikelnr.: 37346836

Inhaltsangabe

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.

Rezensionen

From the reviews:
"This book is the first one exclusively devoted to sequences of associated random variables and the closely related concept of demimartingales. ... The book is well written, with a good balance of theoretical results, applications and examples. Authored by one of the leading experts of the field, it contains the most important results on associated sequences and demimartingales and will become an extremely valuable reference book for researchers in the broad area of association." (Tasos C. Christofides, Mathematical Reviews, November, 2013)