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The research on the local correlation structure of copula function is an attractive topic.This paper investigates bivariate copula function’s local correlation structure by defining its concentration ...
We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbour...
One-sample and multi-sample tests on the concentration parameter of Fisher-von Mises-Langevin (FvML) distributions have been well studied in the literature. However, only very little is known about th...
Concentration-Based Guarantees for Low-Rank Matrix Reconstruction      Low-Rank Matrix Reconstruction         font style='font-size:12px;'> 2011/3/25
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate...
Let $X_1,...,X_n$ be a random sample from some unknown probability density $f$ defined on a compact homogeneous manifold $\mathbf M$ of dimension $d \ge 1$. Consider a 'needlet frame' $\{\phi_{j \eta}...
Let P be any product (Borel) probability measure on product (Polish) space E and for vectors x,y,z in E let f(x,y,z) be the number of coordinates k for which x_k neither equals y_k nor z_k. Using a tr...
We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply ...
A Note on Talagrand's Concentration Inequality     Concentration of measure  empirical processes       font style='font-size:12px;'> 2009/5/4
In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that guarantees the existence of a certain kernel....
We give upper bounds for the probability $P(|f(X)-Ef(X)|>x)$, where $X$ is a stable random variable with index close to 2 and $f$ is a Lipschitz function. While the optimal upper bound is known to be ...
We give a simple development of the concentration properties of compound Poisson measures on the nonnegative integers. A new modification of the Herbst argument is applied to an appropriate modified l...
Measure Concentration for Stable Laws with Index Close to 2      Measure Concentration  Stable Laws  Index       font style='font-size:12px;'> 2009/4/7
We give upper bounds for the probability $P(|f(X)-Ef(X)|>x)$, where $X$ is a stable random variable with index close to 2 and $f$ is a Lipschitz function. While the optimal upper bound is known to be ...
We derive concentration inequalities for functions of the empirical measure of large random matrices with infinitely divisible entries and, in particular, stable ones. We also give concentration res...
Modeling Hourly Ozone Concentration Fields      Dynamic linear model  hierarchical Bayes  ozone  random field  space–time fields       font style='font-size:12px;'> 2010/4/29
This paper presents a dynamic linearmodel for modeling hourly ozone concentrations over the eastern United States. That model, which is developed within an Bayesian hierarchical framework,inherits th...

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