Multivariate Log-Concave Distributions as a Nearly Parametric Model
| Autor: | Lutz Duembgen, Dominic Schuhmacher, Andre Huesler |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Pointwise convergence Weak convergence Laplace transform Gaussian 010102 general mathematics Probability (math.PR) Mathematics - Statistics Theory Statistics Theory (math.ST) 01 natural sciences 010104 statistics & probability Total variation symbols.namesake Modeling and Simulation Parametric model Convergence (routing) symbols FOS: Mathematics Probability distribution Applied mathematics 62A01 62G05 62G07 62G15 62G35 0101 mathematics Statistics Probability and Uncertainty Mathematics - Probability Mathematics |
| Zdroj: | Schuhmacher, Dominic; Hüsler, André; Dümbgen, Lutz (2009). Multivariate Log-Concave Distributions as a Nearly Parametric Model (Technical Report 74). Bern: Institut für mathematische Statistik und Versicherungslehre der Universität Bern (IMSV) Schuhmacher, Dominic; Hüsler, André; Dümbgen, Lutz (2011). Multivariate Log-Concave Distributions as a Nearly Parametric Model. Statistics & risk modeling, 28(3), pp. 277-295. Berlin: Oldenbourg Wissenschaftsverlag GmbH 10.1524/stnd.2011.1073 Statistics and Risk Modeling |
| DOI: | 10.1524/stnd.2011.1073 |
| Popis: | In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. Hence the nonparametric model P_d has similar properties as parametric models such as, for instance, the family of all d-variate Gaussian distributions. Comment: updated two references, changed the local technical report number |
| Databáze: | OpenAIRE |
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