We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya–Watson regression estimator and the conditional empirical process. Our results may be useful to establish uniform consistency of data-driven bandwidth kernel-type function estimators.

The key problem of inductive-learning in Bayes network is the estimator of prior distribution. This paper adopted general native Bayes to handle continuous variables, proposed a kind of kernel function constructed by orthogonal polynomials, which is used to estimate the density function of prior distribution in Bayes network. Paper then made further researches into optimality of kernel density ...

Objective: This paper aims to introduce a modified kernel-type ridge estimator for partially linear models under randomly-right censored data. Such models include two main issues that need to be solved: multi-collinearity and censorship. To address these issues, we improved the kernel estimator based on synthetic data transformation and kNN imputation techniques. The key idea of this paper is t...

We discuss a robust data sharpening method for rendering a standard kernel estimator, with a given bandwidth, unimodal. It has theoretical and numerical properties of the type that one would like such a technique to enjoy. In particular, we show theoretically that, with probability converging to 1 as sample size diverges, our technique alters the kernel estimator only in places where the latter...

Abstract: Density weighted average is a nonparametric quantity expressed by expectation of a function of random variables with density weight. It is associated with parametric components of some semiparametric models, and we are concerned with an estimator of this quantity. Asymptotic properties of semiparametric estimators have been studied in econometrics since the end of 1980’s and it is now...

Abstract. We study an estimator for smoothing irregularly sampled data into a smooth map. The estimator has been widely used in astronomy, owing to its low level of noise; it involves a weight function – or smoothing kernel – w(θ). We show that this estimator is not unbiased, in the sense that the expectation value of the smoothed map is not the underlying process convolved with w, but a convol...

We propose a nonparametric discrimination method based on a nonparametric Nadaray-Watson kernel regression type-estimator of the posterior probability that an incoming observed vector is a given class. To overcome the curse of dimensionality of the multivariate kernel density estimate, we introduce a variance stabilizing approach which constructs independent predictor variables. Then, the multi...

We introduce a new two-step kernel density estimation method, based on the EM algorithm and the generalized kernel density estimator. The accuracy obtained is better in particular, in the case of multimodal or skewed densities.

This paper introduces an object shape representation using Kernel Density Feature Points Estimator (KDFPE). In this method we obtain the density of feature points within defined rings around the centroid of the image. The Kernel Density Feature Points Estimator is then applied to the vector of the image. KDFPE is invariant to translation, scale and rotation. This method of image representation ...

Nonparametric kernel estimators are widely used in many research areas of statistics. An important nonparametric kernel estimator of a regression function is the Nadaraya-Watson kernel regression estimator which is often obtained by using a fixed bandwidth. However, the adaptive kernel estimators with varying bandwidths are specially used to estimate density of the long-tailed and multi-mod dis...