Author | Peรฑa, Vรญctor H. de la. author |
---|---|
Title | Decoupling [electronic resource] : From Dependence to Independence / by Vรญctor H. de la Peรฑa, Evarist Ginรฉ |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0537-1 |
Descript | XV, 392 p. online resource |
1 Sums of Independent Random Variables -- 1.1 Lรฉvy-Type Maximal Inequalities -- 1.2 Hoffmann-J?rgensen Type Inequalities -- 1.3 The KhinchinโKahane Inequalities -- 1.4 Moment Bounds -- 1.5 Estimates with Sharp Constants for the La-Norms of Sums of Independent Random Variables: The L-Function -- 1.6 References for Chapter 1 -- 2 Randomly Stopped Processes With Independent Increments -- 2.1 Waldโs Equations -- 2.2 Good-Lambda Inequalities -- 2.3 Randomly Stopped Sums of Independent Banach-Valued Variables -- 2.4 Proof of the Lower Bound of Theorem 2.3.1 -- 2.5 Continuous Time Processes -- 2.6 BurkholderโGundy Type Inequalities in Banach Spaces -- 2.7 From Boundary Crossing of Nonrandom Functions to First Passage Times of Processes with Independent Increments -- 2.8 References for Chapter 2 -- 3 Decoupling of U-Statistics and U-Processes -- 3.1 Decoupling of U-Processes: Convex Functions -- 3.2 Hypercontractivity of Rademacher Chaos Variables -- 3.3 Minorization of Tail Probabilities: The PaleyโZygmund Argument and a Conditional Jensenโs Inequality -- 3.4 Decoupling of U-processes: Tail Probabilities -- 3.5 Randomization136 -- 3.6 References for Chapter 3 -- 4 Limit Theorems for U-Statistics -- 4.1 Some Inequalities; the Law of Large Numbers -- 4.2 Gaussian Chaos and the Central Limit Theorem for Canonical U-Statistics -- 4.3 The Law of the Iterated Logarithm for Canonical U-Statistics -- 4.4 References for Chapter 4 -- 5 Limit Theorems for U-Processes -- 5.1 Some Background on Asymptotics of Processes, Metric Entropy, and Vapnikโ?ervonenkis Classes of Functions: Maximal Inequalities -- 5.2 The Law of Large Numbers for U-Processes -- 5.3 The Central Limit Theorem for U-Processes -- 5.4 The Law of the Iterated Logarithm for Canonical U-Processes -- 5.5 Statistical Applications -- 5.6 References for Chapter 5 -- 6 General Decoupling Inequalities for Tangent Sequences -- 6.1 Some Definitions and Examples -- 6.2 Exponential Decoupling Inequalities for Sums -- 6.3 Tail Probability andLpInequalities for Tangent Sequences I -- 6.4 Tail Probability and Moment Inequalities for Tangent Sequences II: Good-Lambda Inequalities -- 6.5 Differential Subordination and Applications -- 6.6 Decoupling Inequalities Compared to Martingale Inequalities -- 6.7 References for Chapter 6323 -- 7 Conditionally Independent Sequences -- 7.1 The Principle of Conditioning and Related Results -- 7.2 Analysis of a Sequence of Two-by-Two Tables -- 7.3 SharpLpComparison of Sums of Arbitrarily Dependent Variables to Sums of CI Variables -- 7.4 References for Chapter 7 -- 8 Further Applications of Decoupling -- 8.1 Randomly Stopped Canonical U-Statistics -- 8.2 A General Class of Exponential Inequalities for Martingales and Ratios -- 8.3 References for Chapter 8 -- References