Related papers: Nonparametric functionals as generalized functions
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
In this paper, we are interested in nonparametric kernel estimation of a generalized regression function, including conditional cumulative distribution and conditional quantile functions, based on an incomplete sample $(X_t, Y_t,…
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…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
Descriptive statistics for parametric models are currently highly sensative to departures, gross errors, and/or random errors. Here, leveraging the structures of parametric distributions and their central moment kernel distributions, a…
We address the estimation of conditional quantiles when the covariate is functional and when the order of the quantiles converges to one as the sample size increases. In a first time, we investigate to what extent these large conditional…
We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…
We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while…
This papers presents a generalization of the Weitzman overlapping coefficient, originally defined for two probability density functions, to a setting involving k independent distributions, denoted by Delta. To estimate this generalized…
In this paper we consider the nonparametric estimation of density and regression functions with non-negative support using a gamma kernel procedure introduced by Chen (2000). Strong uniform consistency and asymptotic normality of the…