Related papers: Limit theorems for kernel density estimators under…
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…
In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error rate $n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases where this rate…
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…
The performance of several common approximations for the exchange-correlation kernel within time-dependent density-functional theory is tested for elementary excitations in the homogeneous electron gas. Although the adiabatic local-density…
In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches…
A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
We compute some dependence coefficients for the stationary Markov chain whose transition kernel is the Perron-Frobenius operator of an expanding map $T$ of $[0, 1]$ with a neutral fixed point. We use these coefficients to prove a central…
In this paper, we investigate the almost sure convergence, in supremum norm, of the rank-based linear wavelet estimator for a multivariate copula density. Based on empirical process tools, we prove a uniform limit law for the deviation,…
Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…
We prove finite-sample concentration and anti-concentration bounds for dimension estimation using Gaussian kernel sums. Our bounds provide explicit dependence on sample size, bandwidth, and local geometric and distributional parameters,…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
We define a new bandwidth-dependent kernel density estimator that improves existing convergence rates for the bias, and preserves that of the variation, when the error is measured in $L_1$. No additional assumptions are imposed to the…
In this paper we investigate the kernel estimator of the density for a stationary reversible Markov chain. The proofs are based on a new central limit theorem for a triangular array of reversible Markov chains obtained under conditions…
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$,…
In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…