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.
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