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Discussion of ‘Maximum likelihood estimation of a multi-dimensional log-concave density’ by M. Cule, R. Samworth and M. Stewart
likelihood estimation multi-dimensional log-concave density
2015/8/20
I started looking at log-concave distributions when I was searching for an appropriate model
for subpopulations of multivariate flow cytometry data about ten years ago. The use of log-concave
...
Inference and Modeling with Log-concave Distributions
Log-concave Distributions Inference and Modeling
2015/8/20
Log-concave distributions are an attractive choice for modeling
and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions ...
Clustering with mixtures of log-concave distributions
EM algorithm Log-concave distribution Clustering Normal copula
2015/8/20
The EM algorithm is a popular tool for clustering observations via a parametric mixture model. Two disadvantages of this
approach are that its success depends on the appropriateness of the assumed pa...
Tail estimates for norms of sums of log-concave random vectors
log-concave random vectors concentration inequalities deviation inequalities random matrices
2011/9/15
Abstract: We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the nor...
Concentration of the information in data with log-concave distributions
Concentration entropy log-concave distributions
2011/2/28
A concentration property of the functional −log f(X) is demonstrated,when a random vector X has a log-concave density f on Rn.This concentration property implies in particular an extension of th...
Interpolating Thin-Shell and Sharp Large-Deviation Estimates For Isotropic Log-Concave Measures
Interpolating Thin-Shell Sharp Large-Deviation Estimates Isotropic Log-Concave Measures
2010/11/9
Given an isotropic random vector $X$ with log-concave density in Euclidean space $\Real^n$, we study the concentration properties of $|X|$. We show in particular that: \[ \P(|X| \geq (1+t) \sqrt{n}) ...
Arguments of zeros of highly log concave polynomials
Arguments of zeros highly log concave polynomials
2010/12/14
For a real polynomial p =Pn i=0 cixi with no negative coefficients and n ≥ 6, let β(p) = infn−1 i=1 c2i /ci+1ci−1 (so β(p) ≥ 1 entails that p is log concave). If β(p) > 1.45 . . . , then a...