Multivariate log-concave distributions as a nearly parametric model
Multivariate log-concave distributions as a nearly parametric model
复制标题
作为近参数模型的多元对数凹分布
DOI：
10.1524/stnd.2011.1073
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
J. Wellner
中科院分区：
文献类型：
--
作者：
L. Dümbgen;S. Geer;M. Veraar;J. Wellner
摘要在本文中，我们表明，与对数凸线密度的概率分布的家族PD（LC）尤其满足了强烈的连续性条件。 ，（ii）在此和其他几个方面的趋同的收敛和（iii）在此方面转化了非参数模型PD（LC），例如参数模型，例如所有D-Variate的家族高斯分布是由于连续性结果，我们证明了PD中未知分布的矩（LC）的非平凡置信度。 。
Abstract In this paper we show that the family Pd(lc) of probability distributions on ℝd 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. In this and several other respects the nonparametric model Pd(lc) behaves like a parametric model such as, for instance, the family of all d-variate Gaussian distributions. As a consequence of the continuity result, we prove the existence of nontrivial confidence sets for the moments of an unknown distribution in Pd(lc). Our results are based on various new inequalities for log-concave distributions which are of independent interest.