Associated Sequences, Demimartingales and Nonparametric Inference

- 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

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