Title :
Choice of Kernel Function for Density Estimation
Author :
Kazakos, Dimitri
Author_Institution :
Department of Electrical Engineering, State University of New York at Buffalo, Amherst, NY 14260.
fDate :
5/1/1980 12:00:00 AM
Abstract :
Let l=f^n(x) be the kernel estimate of a density f(x) from a sample of size n. Wahba [6] has developed an upper bound to E[f(x)-l=f^n(x)]2. In the present paper, we find the kernel function of finite support [m=-T, T] that minimizes Wahba´s upper bound. It is Q(y) = (1 + am=-1) (2T)m=-1 [1-m=-a|y|a] where a = 2-pm=-1, p m=ge 1.
Keywords :
Conferences; Educational institutions; Image analysis; Kernel; Pattern classification; Pattern recognition; Random variables; Stochastic processes; Stochastic systems; Upper bound; Density estimation; kernel density estimates; nonparametric estimation;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.1980.4767013
