Related papers: Asymptotic normality of the Parzen-Rosenblatt dens…

Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…

Discrete kernel smoothing is now gaining importance in nonparametric statistics. In this paper, we investigate some asymptotic properties of the normalized discrete associated-kernel estimator of a probability mass function. We show, under…

Bernstein estimators are well-known to avoid the boundary bias problem of traditional kernel estimators. The theoretical properties of these estimators have been studied extensively on compact intervals and hypercubes, but never on the…

We establish asymptotic normality of weighted sums of periodograms of a stationary linear process where weights depend on the sample size. Such sums appear in numerous statistical applications and can be regarded as a discretized versions…

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…

We establish asymptotic normality for estimators of the additive regression components under random censorship. To build our estimators, we couple the marginal integration method (Newey (1994)) with an initial Inverse Probability of…

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…

We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the $d$-dimensional simplex. The simplex is an important case as…

The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…

We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…

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),…

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…

In this study, we develop an asymptotic theory of nonparametric regression for locally stationary random fields (LSRFs) $\{{\bf X}_{{\bf s}, A_{n}}: {\bf s} \in R_{n} \}$ in $\mathbb{R}^{p}$ observed at irregularly spaced locations in…

We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction…

Nonparametric density estimation is of great importance when econometricians want to model the probabilistic or stochastic structure of a data set. This comprehensive review summarizes the most important theoretical aspects of kernel…

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered…

We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil (1994). We study the properties of these estimators and compare…

Let $X_1,...,X_n$ be i.i.d. observations, where $X_i=Y_i+\sigma_n Z_i$ and the $Y$'s and $Z$'s are independent. Assume that the $Y$'s are unobservable and that they have the density $f$ and also that the $Z$'s have a known density $k.$…

We consider estimating the density of a response conditioning on an error-prone covariate. Motivated by two existing kernel density estimators in the absence of covariate measurement error, we propose a method to correct the existing…