B.L.S. Prakasa Rao
Springer Basel
2012e druk, 2011
9783034802390
Associated Sequences, Demimartingales and Nonparametric Inference
Specificaties
Gebonden, 272 blz.
|
Engels
Springer Basel |
2012e druk, 2011
ISBN13: 9783034802390
Rubricering
Onderdeel van serie
Probability and Its Applications
Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
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.
Specificaties
ISBN13:9783034802390
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:272
Uitgever:Springer Basel
Druk:2012
Inhoudsopgave
<p>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.</p>