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eISBN : 9781461448693

Sommaire : 1 Main Directions in the Theory of ProbabilityMetrics

Part I General Topics in the Theory of ProbabilityMetrics

2 Probability Distances and ProbabilityMetrics: Definitions
3 Primary, Simple, and Compound Probability Distances
4 A Structural Classification of Probability Distances
References

Part II Relations Between Compound, Simple, and Primary Distances

5 Monge–Kantorovich Mass Transference Problem, Minimal Distances and Minimal Norms
References
6 Quantitative Relationships Between Minimal Distances and Minimal Norms
7 K-Minimal Metrics
References
8 Relations Between Minimal and Maximal Distances
Reference
9 Moment Problems Related to the Theory of Probability Metrics: Relations Between Compound and Primary Distances
References

Part III Applications of Minimal Probability Distances

10 Moment Distances
References
11 Uniformity inWeak and Vague Convergence
References
12 Glivenko–Cantelli Theorem and Bernstein–Kantorovich Invariance Principle
References
13 Stability of Queueing Systems
References
14 Optimal Quality Usage

Part IV Ideal Metrics

15 Ideal Metrics with Respect to Summation Scheme for i.i.d. Random Variables
References
16 Ideal Metrics and Rate of Convergence in the CLT for Random Motions
References
17 Applications of Ideal Metrics for Sums of i.i.d. Random
References
18 How Close Are the Individual and Collective Models in Risk Theory?
References
19 Ideal Metric with Respect to Maxima Scheme of i.i.d. Random Elements
References
20 Ideal Metrics and Stability of Characterizations of Probability Distributions
References

Part V Euclidean-Like Distances and Their Applications

21 Positive and Negative Definite Kernels and Their Properties
References
22 Negative Definite Kernels and Metrics: Recovering Measures from Potentials
References
23 Statistical Estimates Obtained by the Minimal Distances Method
References
24 Some Statistical Tests Based on N-Distances
References
25 Distances Defined by Zonoids
References
26 N-Distance Tests of Uniformity on the Hypersphere
References
About the Authors
Index

Langue : Anglais

Localisation : Bibliothèque Campus de Nice

Support : Numérique

Etat : Présent

Professeur EDHEC : Oui

Propriétaire : Bibliothèque