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Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…
In this paper, we consider the deformed Fredholm determinant of the confluent hypergeometric kernel. This determinant represents the gap probability of the corresponding determinantal point process where each particle is removed…
In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…
Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…
We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…
In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be…
We obtain "large gap" asymptotics for a Fredholm determinant with a confluent hypergeometric kernel. We also obtain asymptotics for determinants with two types of Bessel kernels which appeared in random matrix theory.
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
We show that under very general assumptions the partial Bergman kernel function of sections vanishing along an analytic hypersurface has exponential decay in a neighborhood of the vanishing locus. Considering an ample line bundle, we obtain…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…
We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. First, we provide results that give upper estimates in a situation when the corresponding jump measure is allowed to be highly…
This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$ norm…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…