Page 311 - Introduction to Statistical Pattern Recognition
P. 311
6 Nonparametric Density Estimation 293
(6.151)
then the basis function of (6.141) becomes
(6.152)
where
(6.153)
which is the normalized y,.
On the other hand, the kernel of (6.142) becomes
(6.154)
If the y, 's are mutually independent, p (Y) becomes equal to K(Y).
Thus, we can find the expansion of p (Y) as
(6.155)
where the first term K(Y) equals p (Y) under the independence assumption, and
all other terms of [.] are the correction terms. The cj's are calculated by
(6.156)
Thus, (6.155) becomes
where y's are the correlation coefficients of the associated variables.
(6.158)
