Related papers: S-inequality for certain product measures
We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the…
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
Studying overlapping coefficients has recently become of great benefit, especially after its use in goodness-of-fit tests. These coefficients are defined as the amount of similarity between two statistical distributions. This research…
A generalisation of the Cassels and Greub-Reinboldt inequalities in complex or real inner product spaces and applications for isotonic linear functionals, integrals and sequences are provided.
We give an equivalence-singularity criterion for infinite products of Cauchy measures under simultaneous shifts of the location and scale parameters. Our result is an extension of Lie and Sullivan's result giving an equivalence-singularity…
We establish analogs of Cheeger's inequality for probability measures with heavy tails. As one of the principal applications, suppose $\lambda > 3$ and define the (Pareto) probability measure $\mu_{\lambda}$ on $[1,\infty)$ by…
Income inequality measures are often used as an indication of economic health. How to obtain reliable confidence intervals for these measures based on sampled data has been studied extensively in recent years. To preserve confidentiality,…
Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…
We present a new method for proving the norm concentration inequality of sub-Gaussian variables. Our proof is based on an averaged version of the moment generating function, termed the averaged moment generating function. Our method applies…
By recognizing that the main difficulty of the modeling of daily precipitation amounts is the selection of an appropriate probability distribution, this study aims to establish a model selection framework to identify the appropriate…
Inequality (concentration) curves such as Lorenz, Bonferroni, Zenga curves, as well as a new inequality curve -- the $D$ curve, are broadly used to analyse inequalities in wealth and income distribution in certain populations. Quantile…
In this paper, we give a detailed survey on norm inequalities for inner product type integral transformers. We first consider unitarily invariant norms and operator valued functions. We then give results on norm inequalities for inner…
We prove several estimates for the moments of arbitrary measures on convex bodies. We apply these estimates to show a new slicing inequality for measures on convex bodies. We also deduce estimates for the outer volume ratio distance from an…
Recent development in high-dimensional statistical inference has necessitated concentration inequalities for a broader range of random variables. We focus on sub-Weibull random variables, which extend sub-Gaussian or sub-exponential random…
We analyse non ideal quantum measurements described as scattering processes providing an estimator of the measured quantity. The sensitivity is expressed as an equivalent input noise. We address the Von Neumann problem of chained…
Probabilities of measurement outcomes of two-particle entangled states give a physically transparent interpretation of the concurrence and of the I-concurrence as entanglement measures. The (I)-concurrence can thus be measured…
Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated…
We introduce a quantitative version of Property A in order to estimate the L^p-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential volume growth. This quantitative property A also appears to…
The proposed paper discusses the problem of discrimination between close hypotheses about distributions belonging to the Gumbel maximum domain of attraction. The distinctive feature of the proposed work is using only k higher order…
In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider…