Abstract: In the this paper, the authors propose to estimate the density of a targeted population with a weighted kernel density estimator (wKDE) based on a weighted sample. Bandwidth selection for wKDE is discussed. Three mean integrated squared error based bandwidth estimators are introduced and their performance is illustrated via Monte Carlo simulation. The least-squares cross-validation me...

We consider the problem of uniform asymptotics in kernel functional estimation where the bandwidth can depend on the data. In a unified approach we investigate kernel estimates of the density and the hazard rate for uncensored and right-censored observations. The model allows for the fixed bandwidth as well as for various variable bandwidths, e.g. the nearest neighbor bandwidth. An elementary p...

In order to obtain reference curves for data sets when the covariate is multidimensional, we propose in this paper a new procedure based on dimension-reduction and nonparametric estimation of conditional quantiles. This semiparametric approach combines sliced inverse regression (SIR) and a kernel estimation of conditional quantiles. The asymptotic convergence of the derived estimator is shown. ...

In this paper, a class of estimators of the center of symmetry based on the empirical characteristic function is examined. In the spirit of the Hodges-Lehmann estimator, the resulting procedures are shown to be a function of the pairwise averages. The proposed procedures are also shown to have an equivalent representation as the minimizers of certain distances between two corresponding kernel d...

In order to obtain reference curves for data sets when the covariate is multidimensional, we propose a new methodology based on dimension-reduction and nonparametric estimation of conditional quantiles. This semiparametric approach combines sliced inverse regression (SIR) and a kernel estimation of conditional quantiles. The convergence of the derived estimator is shown. By a simulation study, ...

Abstract : In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the unidimensional case for the Nadaraya-Watson estimator. Moreover, we giv...

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 ...

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the ...

In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift problem, we derive high probability confidence bounds for the kernel mean matching (KMM) estimator, whose convergence rate turns out to depend on some regularity...

The paper establishes the conditions under which the generalised least squares estimator of the regression parameters is equivalent to the weighted least squares estimator. The equivalence conditions have interesting applications in local polynomial regression and kernel smoothing. Specifically, they enable to derive the optimal kernel associated with a particular covariance structure of the me...