Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and finite sample performance conditional on the shape of the density near zero and the exact form of the cho...

A neural network architecture for clustering and classification is described. The Adaptive Kernel Neural Network (AKNN) is a density estimation technique closely related to kernel estimation. The accompanying learning scheme adjusts the connection weights, activation functions, and the number of nodes in the network. The network, as described here, is made up of three layers of nodes: the input...

In data analytic applications of density estimation one is usually interested in estimating the density over its support. However, common estimators such as the basic kernel estimator use a single smoothing parameter over the whole of the support. While this will be adequate for some densities there will be other densities that will be very difficult to estimate using this approach. The purpose...

-We develop a method of performing pattern recognition (discrimination and classification) using a recursive technique derived from mixture models, kernel estimation and stochastic approximation. Unsupervised learning Density estimation Kernel estimator Mixture model Stochastic approximation Recursive estimation

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected...

We construct a density estimator and an estimator of the distribution function in the uniform deconvolution model. The estimators are based on inversion formulas and kernel estimators of the density of the observations and its derivative. Asymptotic normality and the asymptotic biases are derived. AMS classification: primary 62G05; secondary 62E20, 62G07, 62G20

Abstract: In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behaviour not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the unifor...

In this paper we provide a detailed characterization of the asymptotic behavior of kernel density estimators for one-sided linear processes. The conjecture that asymptotic normality for the kernel density estimator holds under short-range dependence is proved under minimal assumptions on bandwidths. We also depict the dichotomous and trichotomous phenomena for various choices of bandwidths when...