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Choice of Kernel Function for Density Estimation

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1 Author(s)
Dimitri Kazakos ; Department of Electrical Engineering, State University of New York at Buffalo, Amherst, NY 14260.

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.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:PAMI-2 ,  Issue: 3 )