Related papers: Sharp Large Deviations for empirical correlation c…
Gaussian copulas are widely used to estimate multivariate distributions and relationships. We present algorithms for estimating Gaussian copula correlations that ensure differential privacy. We first convert data values into sets of two-way…
We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm.
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
We obtain large deviations estimates for systems with stretched exponential decay of correlations, which improve the ones obtained in \cite{AFLV11}. As a consequence we obtain better large deviations estimates for Viana maps and get large…
The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of…
The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
We investigate the small deviation probabilities of a class of very smooth stationary Gaussian processes playing an important role in Bayesian statistical inference. Our calculations are based on the appropriate modification of the entropy…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds…
In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…
Large deviation inequalities for ergodic sums is an important subject since the seminal contribution of Bernstein for independent random variables with finite variances, followed by the Chernoff method and the Hoefding result for…
Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…
In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…
Through computer simulations, we research several different measures of dependence, including Pearson's and Spearman's correlation coefficients, the maximal correlation, the distance correlation, a function of the mutual information called…
We obtain large deviation results for a two time-scale model of jump-diffusion processes. The processes on the two time scales are fully inter-dependent, the slow process has small perturbative noise and the fast process is ergodic. Our…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…