相关论文: Signed variable optimal kernel for non-parametric …

Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…

We propose nonparametric estimation of divergence measures between continuous distributions. Our approach is based on a plug-in kernel- type estimators of density functions. We give the uniform in bandwidth consistency for the proposal…

We consider the nonparametric estimation of the univariate heavy tailed probability density function (pdf) with a support on $[0,\infty)$ by independent data. To this end we construct the new kernel estimator as a combination of the…

We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we…

This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…

The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…

A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel functions, the coefficients of which are determined by a linear…

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,…

Given a sample from a discretely observed compound Poisson process, we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. An order bound for…

Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…

We constraint on computer the best linear unbiased generalized statistics of random field for the best linear unbiased generalized statistics of an unknown constant mean of random field and derive the numerical generalized least-squares…

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 derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio…

We prove that the optimal assignment kernel, proposed recently as an attempt to embed labeled graphs and more generally tuples of basic data to a Hilbert space, is in fact not always positive definite.

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…

Simulation models of complex dynamics in the natural and social sciences commonly lack a tractable likelihood function, rendering traditional likelihood-based statistical inference impossible. Recent advances in machine learning have…

Bandwidth selection is crucial in the kernel estimation of density level sets. A risk based on the symmetric difference between the estimated and true level sets is usually used to measure their proximity. In this paper we provide an…

Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…