Multivariate Log-Concave Distributions as a Nearly Parametric Model

Details Multivariate Log-Concave Distributions as a Nearly Parametric Model Multivariate Log-Concave Distributions as a Nearly Parametric Model

2009-07-01

arxiv.org/abs/0907.0250v3

Statistics and Risk Modeling, Volume 28, Number 3 (2011), pp. 277-295

Mathematics

Probability

updated two references, changed the local technical report number

Scientific paper

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.

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