It is now common practice in machine vision to define the variability in an object’s appearance in a factored manner, as a combination of shape and texture transformations. In this context, we present a simple and practical method for estimating non-parametric probability densities over a group of linear shape deformations. Samples drawn from such a distribution do not lie in a Euclidean space,...

Abstract. In this paper, we study the estimation of a function based on noisy inhomogeneous data (the amount of data can vary on the estimation domain). We consider the model of regression with random design, where the design density is unknown. We construct an asymptotically sharp estimator which converges, for sup norm error loss, with a spatially dependent normalisation which is sensitive to...

We consider estimation of the common probability density f of i.i.d. random variables Xi that are observed with an additive i.i.d. noise. We assume that the unknown density f belongs to a class A of densities whose characteristic function is described by the exponent exp(−α|u|r) as |u| → ∞, where α > 0, r > 0. The noise density is supposed to be known and such that its characteristic function d...

We present a semi-parametric deconvolution estimator for the density function of a random variable biX that is measured with error, a common challenge in many epidemiological studies. Traditional deconvolution estimators rely only on assumptions about the distribution of X and the error in its measurement, and ignore information available in auxiliary variables. Our method assumes the availabil...

The number of modes (also known as modality) of a kernel density estimator (KDE) draws lots of interests and is important in practice. In this paper, we develop an inference framework on the modality of a KDE under multivariate setting using Gaussian kernel. We applied the modal clustering method proposed by [1] for mode hunting. A test statistic and its asymptotic distribution are derived to a...

This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators...

We have previously proposed the use of quadratic Renyi’s error entropy with a Parzen density estimator with Gaussian kernels as an alternative optimality criterion for supervised neural network training, and showed that it produces better performance on the test data compared to the MSE. The error entropy criterion imposes the minimization of average information content in the error signal rath...

Pruitt (1991b) proposed estimating a bivariate survival function for censored data by modifying the self-consistency equations of the EM-algorithm. Though not efficient, the estimator has very good practical performance. In this paper, we prove weak convergence at √ n-rate, strong uniform consistency and a semiparametric bootstrap result for this implicitly defined estimator. The estimator is a...

We present a nonparametric method for galaxy clustering in astronomical sky surveys. We show that the cosmological definition of clusters of galaxies is equivalent to density contour clusters (Hartigan , 1975) Sc = {f > c} where f is a probability density function. The plug-in estimator Ŝc = {f̂ > c} is used to estimate Sc where f̂ is the multivariate kernel density estimator. To choose the optim...