Related papers: Bias correction and uniform inference for the quan…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

Kernel density estimation and kernel regression are powerful but computationally expensive techniques: a direct evaluation of kernel density estimates at $M$ evaluation points given $N$ input sample points requires a quadratic…

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…

The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$,…

In this paper we establish asymptotic simultaneous confidence bands for the transformation kernel estimator of copulas introduced in Omelka et al.(2009). To this aim, we prove a uniform in bandwidth law of the iterated logarithm for the…

In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…

It is shown that the Hall, Hu and Marron [Hall, P., Hu, T., and Marron J.S. (1995), Improved Variable Window Kernel Estimates of Probability Densities, {\it Annals of Statistics}, 23, 1--10] modification of Abramson's [Abramson, I. (1982),…

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…

Consider a Gaussian nonparametric regression problem having both an unknown mean function and unknown variance function. This article presents a class of difference-based kernel estimators for the variance function. Optimal convergence…

We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…

For a multidimensional It\^o semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated…

The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset…

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…

Kernel estimation techniques, such as mean shift, suffer from one major drawback: the kernel bandwidth selection. The bandwidth can be fixed for all the data set or can vary at each points. Automatic bandwidth selection becomes a real…

There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and…

This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample…

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation…

In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…

An important challenge in statistical analysis lies in controlling the bias of estimators due to the ever-increasing data size and model complexity. Approximate numerical methods and data features like censoring and misclassification often…