Page 222 - Introduction to Statistical Pattern Recognition

204 Introduction to Statistical Pattern Recognition

Thus, discarding terms of higher order than 2,

(5.67)

(5.68)

Note that Ed( Ayi ] = 0, assuming that unbiased estimates are used. Substitut-
ing (5.67) and (5.68) into (5.65),

Furthermore, if the parameters come from M,, M,, XI, and X2 of two normal
distributions, as in (5. lo), G becomes

A
Equation (5.69) is a very general expression for the bias of the error, which is
valid regardless of the selection of h (X), PI, and pI (X). The term E [ Ay,Ay, ]
gives the effect of the sample size, YL. Therefore, if (5.5) is satisfied, can be
expressed by vg (E) where v is determined by h (X), PI, and p,(X), and the
estimation procedure of (5.6) can be applied. Furthermore, if h(X) is a func-