Set up the classification problem .
 Bayes  rule.
Nonparametric density estimation.
histogram
Derive bias and variance for kernel estimates.
 Cross-validation (pretend that the kernel estimation is
a one parameter family, m.l.e.)
Plug-in method :  needs crude estimate of  higher order derivative of density (used in bias caculation).

Bias ^2 = h^{-2}
variance = 1/n h^p
optimal rate = 1/ n^{2/(2+p)} ; slow for high dim. density.

See last Friday's p.d.f.