Related papers: Kernel Density Estimation Bias under Minimal Assum…
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…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…
Blind image deblurring algorithms have been improving steadily in the past years. Most state-of-the-art algorithms, however, still cannot perform perfectly in challenging cases, especially in large blur setting. In this paper, we focus on…
For the kernel estimator of the quantile density function (the derivative of the quantile function), I show how to perform the boundary bias correction, establish the rate of strong uniform consistency of the bias-corrected estimator, and…
Blind deconvolution problems are severely ill-posed because neither the underlying signal nor the forward operator are not known exactly. Conventionally, these problems are solved by alternating between estimation of the image and kernel…
Estimating the data uncertainty in regression tasks is often done by learning a quantile function or a prediction interval of the true label conditioned on the input. It is frequently observed that quantile regression -- a vanilla algorithm…
A kernel density estimator for data on the polysphere $\mathbb{S}^{d_1}\times\cdots\times\mathbb{S}^{d_r}$, with $r,d_1,\ldots,d_r\geq 1$, is presented in this paper. We derive the main asymptotic properties of the estimator, including mean…
We consider kernel estimators of the instantaneous frequency of a slowly evolving sinusoid in white noise. The expected estimation error consists of two terms. The systematic bias error grows as the kernel halfwidth increases while the…
A kernel density is an aggregate of kernel functions, which are itself densities and could be kernel densities. This is used to decompose a kernel into its constituent parts. Pearson's test for equality of proportions is applied to…
Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel…
Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
In this paper we consider the kernel estimators of a distribution function defined by the stochastic approximation algorithm when the observation are contamined by measurement errors. It is well known that this estimators depends heavily on…
The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…
We introduce \emph{topological density estimation} (TDE), in which the multimodal structure of a probability density function is topologically inferred and subsequently used to perform bandwidth selection for kernel density estimation. We…
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient…