Associated Sequences, Demimartingales and Nonparametric Inference (eBook)

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.