The methods of distances in the theory of probability and statistics
This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to...
שמור ב:
| Auteurs principaux: | , , , |
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| פורמט: | Livre numérique |
| שפה: | Anglais |
| יצא לאור: |
New York, NY :
Springer New York
2013.
Cham : Springer Nature |
| גישה מקוונת: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| הערה: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The methods of distances in the theory of probability and statistics, Svetlozar T. Rachev, Lev B. Klebanov, Stoyan V. Stoyanov... [et al.], New York, Springer, 2013, 1 vol. (XVI-619 p.), 978-1-4614-4868-6 |
תוכן הענינים:
- Main directions in the theory of probability metrics Probability distances and probability metrics: Definitions Primary, simple and compound probability distances, and minimal and maximal distances and norms A structural classification of probability distances.-Monge-Kantorovich mass transference problem, minimal distances and minimal norms Quantitative relationships between minimal distances and minimal norms K-Minimal metrics Relations between minimal and maximal distances Moment problems related to the theory of probability metrics: Relations between compound and primary distances Moment distances Uniformity in weak and vague convergence Glivenko-Cantelli theorem and Bernstein-Kantorovich invariance principle Stability of queueing systems.-Optimal quality usage Ideal metrics with respect to summation scheme for i.i.d. random variables Ideal metrics and rate of convergence in the CLT for random motions Applications of ideal metrics for sums of i.i.d. random variables to the problems of stability and approximation in risk theory How close are the individual and collective models in risk theory?- Ideal metric with respect to maxima scheme of i.i.d. random elements Ideal metrics and stability of characterizations of probability distributions Positive and negative de nite kernels and their properties Negative definite kernels and metrics: Recovering measures from potential Statistical estimates obtained by the minimal distances method Some statistical tests based on N-distances Distances defined by zonoids N-distance tests of uniformity on the hypersphere.-