Inequalities and extremal problems in probability and statistics : selected topics /
editor and contributing author: Iosif Pinelis ; contributing authors: Victor H. de la Peña, Rustam Ibragimov, Adam Osȩkowski, Irina Shevtsova.
- ix;187pages;
Includes bibliographical references.
2.2 On Optimal Stopping of a Process and Its Maximal Function2.3 A Family of Important Examples; 2.4 Proof of Theorem 2.1.1; 2.4.1 On the Search for Φ; 2.4.2 Proof of Theorem 2.1.1; 2.5 Proof of Theorem 2.1.2; 2.5.1 An Auxiliary Optimal Stopping Problem; 2.5.2 Formal Proof of (2.1.6); References; Chapter 3: On the Absolute Constants in Nagaev-Bikelis-Type Inequalities; 3.1 Introduction and Formulation of the Main Results; 3.1.1 Notation; 3.1.2 A Short Historical Review of the Uniform Estimates; 3.1.3 Nonuniform Estimates: History, Problem Statements, Formulation of the New Results. 4.3.2 Possible Improvements of Nagaev's Method4.4 A New Way to Obtain Nonuniform BE Bounds; A quick proof of Nagaev's nonuniform BE bound (4.3.1); 4.5 Constructions of the Smoothing Filter M; 4.6 Another Construction of Smoothing Inequalities for Nonuniform BE Bounds; A quicker proof of Nagaev's nonuniform BE bound (4.3.1); References; Chapter 5: On the Berry-Esseen Bound for the Student Statistic; 5.1 Summary and Discussion; 5.2 Proofs; References; Chapter 6: Sharp Probability Inequalities for Random Polynomials, Generalized Sample Cross-Moments, and Studentized Processe; 6.1 Introduction. 6.2 Sharp Probability Inequalities for Sums of Independent R.V.'s and Their Self-Normalized Analogs6.3 Main Inequalities; 6.3.1 Inequalities for Random Polynomials, Generalized Sample Cross-Moments, and Their Self-Normalized and Studentized Ver ... ; 6.3.2 Extensions of the Results in Sections 6.2 and 6.3.1 to the Case of Dependent R.V.'s ThroughMeasures of Dependence; 6.3.3 Sharp Moment Inequalities for Random Polynomials, Sample Cross-Moments, and Their Applications; 6.4 Applications in Hypothesis Testing; 6.4.1 Permutation Tests Against Serial Correlationand Tests for Independence.