Associated Sequences, Demimartingales and Nonparametric Inference by B.L.S. Prakasa RaoAssociated Sequences, Demimartingales and Nonparametric Inference by B.L.S. Prakasa Rao

Associated Sequences, Demimartingales and Nonparametric Inference

byB.L.S. Prakasa Rao

Paperback | January 26, 2014

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This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.
Title:Associated Sequences, Demimartingales and Nonparametric InferenceFormat:PaperbackDimensions:272 pagesPublished:January 26, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034807465

ISBN - 13:9783034807463

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Table of Contents

Preface.-1. Associated Random Variables and Related Concepts.- Introduction.- Some Probabilistic Properties of Associated Sequences.- Related Concepts of Association.-2. Demimartingales.- Introduction.- Characteristic Function Inequalities.- Doob Type Maximal Inequality.- An Upcrossing Inequality.- Chow Type Maximal Inequality.- Whittle Type Maximal Inequality.- More on Maximal Inequalities.- Maximal phi-Inequalities for Nonnegative Demisubmartingales.- Maximal Inequalities for Functions of Demisubmartingales.- Central Limit Theorems.- Dominated Demisubmartingales.-3. N-Demimartingales.- Introduction.- Maximal Inequalities.- More on Maximal Inequalities.- Downcrossing Inequality.- Chow Type Maximal Inequality.- Functions of N-Demimartingales.- Strong Law of Large Numbers.- Azuma Type Inequality.- Marcinkiewicz-Zygmund Type inequality.- Comparison Theorem on Moment Inequalities.-4. Conditional Demimartingales.- Introduction.- Conditional Independence.- Conditional Association.- Conditional Demimartingales.-5. Multidimensionally Indexed Demimartingales and Continuous Parameter Demimartingales.- Introduction.- Multidimensionally Indexed Demimartingales.- Chow Type Maximal Inequality for Two-parameter Demimartingales.- Continuous Parameter Demisubmartingales.- Maximal inequality for Continuous Parameter Demisubmartingales.- Upcrossing Inequality.-6. Limit Theorems for Associated Random Variables.- Introduction.- Covariance Inequalities.- Hajek-Renyi Type Inequalities.- Exponential Inequality.- Non-uniform and Uniform Berry-Esseen Type Bounds.- Limit Theorems for U-statistics.- More Limit Theorems for U-statistics.- Application to Two-sample Problem.- Limit Theorems for V-statistics.- Limit Theorems for Associated Random Fields.- Remarks.-7. Nonparametric Estimation for Associated Sequences.- Introduction.- Nonparametric Estimation for Survival Function.- Nonparametric Density Estimation.- Nonparametric Failure Rate Estimation.- Nonparametric Mean Residual Life Function Estimation.- Remarks.-8. Nonparametric Tests for Associated Sequences.- Introduction.- More on Covariance Inequalities.- Tests for Location.- Mann-Whitney Test.-9. Nonparametric Tests for Change in Marginal Density Function for Associated Sequences.- Introduction.- Tests for Change Point.- Test for Change in Marginal Density Function.- References.- Index.