相关论文: Uniform in bandwidth consistency of kernel-type fu…

We generalize a method for proving uniform in bandwidth consistency results for kernel type estimators developed by the two last named authors. Such results are shown to be useful in establishing consistency of local polynomial estimators…

We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…

We establish uniform-in-bandwidth consistency for kernel-type estimators of the differential entropy. We consider two kernel-type estimators of Shannon's entropy. As a consequence, an asymptotic 100% confidence interval of entropy is…

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…

In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds for…

In this paper we establish the uniform in bandwidth consistency for the transformation kernel estimator of copulas introduced in [Omelka et al.(2009)]. To this end, we first prove a uniform in bandwidth law of the iterated logarithm for the…

This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are…

We investigate the issue of bandwidth estimation in a nonparametric functional regression model with function-valued, continuous real-valued and discrete-valued regressors under the framework of unknown error density. Extending from the…

In this paper we propose a variable bandwidth kernel regression estimator for $i.i.d.$ observations in $\mathbb{R}^2$ to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of $O(h_n^4)$ under the condition…

Given an i.i.d sample $(Y_i,Z_i)$, taking values in $\RRR^{d'}\times \RRR^d$, we consider a collection Nadarya-Watson kernel estimators of the conditional expectations $\EEE(<c_g(z),g(Y)>+d_g(z)\mid Z=z)$, where $z$ belongs to a compact set…

This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…

We adress the problem of consistency of the $k$-nearest neighbors kernel estimators of the density and the regression function in the multivariate case. We get the rates of strong uniform consistency on the whole space $\mathbb{R}^p$ for…

This paper derives limit properties of nonparametric kernel regression estimators without requiring existence of density for regressors in $\mathbb{R}^{q}.$ In functional regression limit properties are established for multivariate…

Consistency of the kernel density estimator requires that the kernel bandwidth tends to zero as the sample size grows. In this paper we investigate the question of whether consistency is possible when the bandwidth is fixed, if we consider…

Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these…

Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…

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…

Dyadic data is often encountered when quantities of interest are associated with the edges of a network. As such it plays an important role in statistics, econometrics and many other data science disciplines. We consider the problem of…

We extend balloon and sample-smoothing estimators, two types of variable-bandwidth kernel density estimators, by a shift parameter and derive their asymptotic properties. Our approach facilitates the unified study of a wide range of density…