arXiv subjects

Zhen Wai Olivier Ho

Publications and source records attributed to Zhen Wai Olivier Ho.

2 recordsLinked to original sources

arXiv2017

Simple models for multivariate regular variations and the Hüsler-Reiss Pareto distribution

We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman Lemma. This allows us to recover in a simple framework the most popular multivariate extreme value distributions, such as the logistic, negative logistic, Dirichlet, extremal-$t$ and Hüsler-Reiss models. In a second part of the paper, we focus on the Hüsler-Reiss Pareto model and its surprising exponential family property. After a thorough study of this exponential family structure, we focus on maximum likelihood estimation. We also consider the generalized Hüsler-Reiss Pareto model with different tail indices and a likelihood ratio test for discriminating constant tail index versus varying tail indices.

stat.ME↗

arXiv2016

Small coherence implies the weak Null Space Property

In the Compressed Sensing community, it is well known that given a matrix $X \in \mathbb R^{n\times p}$ with $\ell_2$ normalized columns, the Restricted Isometry Property (RIP) implies the Null Space Property (NSP). It is also well known that a small Coherence $μ$ implies a weak RIP, i.e. the singular values of $X_T$ lie between $1-δ$ and $1+δ$ for "most" index subsets $T \subset \{1,\ldots,p\}$ with size governed by $μ$ and $δ$. In this short note, we show that a small Coherence implies a weak Null Space Property, i.e. $\Vert h_T\Vert_2 \le C \ \Vert h_{T^c}\Vert_1/\sqrt{s}$ for most $T \subset \{1,\ldots,p\}$ with cardinality $|T|\le s$. We moreover prove some singular value perturbation bounds that may also prove useful for other applications.

math.ST↗