A novel approach is proposed for density estimation on a network. Nonparametric network formulated as nonparametric regression problem by binning. using local polynomial kernel-weighted least squares have been studied rigorously, and its asymptotic properties make it superior to kernel estimators such the Nadaraya–Watson estimator. When applied network, best estimator near vertex depends amount...

Local vehicle density estimation is increasingly becoming an essential factor of many vehicular ad-hoc network applications such as congestion control and traffic state estimation. This estimation is used to get an approximate number of neighbors within the transmission range since beacons do not give accurate accuracy about neighborhood. These is due to the special characteristics of VANETs su...

Let X|μ ∼ Np(μ,vxI ) and Y |μ ∼ Np(μ,vyI ) be independent pdimensional multivariate normal vectors with common unknown mean μ. Based on observing X = x, we consider the problem of estimating the true predictive density p(y|μ) of Y under expected Kullback–Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Baye...

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose an l1-minimization under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global coher...

Andrew R. Barron Department of Statistics Yale University P.O. Box 208290 New Haven, CT 06520 Andrew. Barron@yale. edu Gaussian mixtures (or so-called radial basis function networks) for density estimation provide a natural counterpart to sigmoidal neural networks for function fitting and approximation. In both cases, it is possible to give simple expressions for the iterative improvement of pe...

We focus on solving the problem of learning an optimal smoothing kernel for the unsupervised learning problem of kernel density estimation(KDE) by using hyperkernels. The optimal kernel is the one which minimizes the regularized negative leave-one-out-log likelihood score of the train set. We demonstrate that ”fixed bandwidth” and ”variable bandwidth” KDE are special cases of our algorithm.