Related papers: Uniform Convergence of Multivariate Spectral Densi…
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…
Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…
Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for…
Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…
The problem of optimal linear estimation of linear functionals depending on the unknown values of a periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
The paper presents new simple sharp bounds for transition density functions for time-homogeneous diffusions processes. The bounds are obtained under mild conditions on the drift and diffusion coefficients, extending and substantially…
Convergence rate estimates in limit theorems for sums of independent random variables are considered.
The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of…
This paper addresses the problem of estimating a convex regression function under both the sup-norm risk and the pointwise risk using B-splines. The presence of the convex constraint complicates various issues in asymptotic analysis,…
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
The estimation of probability density functions (PDF) using approximate maps is a fundamental building block in computational probability. We consider forward problems in uncertainty quantification: the inputs or the parameters of a…
In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…
In this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an $L$-smooth function. We establish a new convergence rate, and show that the bound may be…
We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…
We present a novel algorithm to compute the density of states, which is proven to converge to the correct result. The algorithm is very general and can be applied to a wide range of models, in the frameworks of Statistical Mechanics and…
In this article, the complete moment convergence for the partial sum of moving average processes $\{X_n=\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\ge 1\}$ is estabished under some proper conditions, where $\{Y_i,-\infty<i<\infty\}$ is a sequence…
We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…
Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
We consider the convergence of the empirical spectral measures of random $N \times N$ unitary matrices. We give upper and lower bounds showing that the Kolmogorov distance between the spectral measure and the uniform measure on the unit…