Page 248 - Introduction to Statistical Pattern Recognition

230 Introduction to Statistical Pattern Recognition

1
ifL GIR - -(Y-M), (5.138)
N
1
iL E& + -[[c - (Y-M)(Y-M)T] . (5.139)
N
Now, let us consider the problem of estimating f (M,C) by f(if~,iz),

where f is a given function and Z is either R or L, depending on which esti-
mates are used. The estimate f (kz,&) may be expanded by a Taylor series
around f (M, C) as

afT
f (kz,&) (M,C) + -(Mz A - M) + tr (5.140)
Ef
aM
where

(5.141)

Then, the difference between f (ifL,&) and f(ifR,&) is

= f(kL,%,) -j~ifR,iR)

E -- afr (AML-AMR) + tr
aM

(5.142)

where AM, = if, - M and AXz = iZ C (Z = R or L).
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