Page 235 - Introduction to Statistical Pattern Recognition

5 Parameter Estimation 217

-
E= PIE, + P2E2 . (5.102)

This average error is the same as the error of (5.64). That is, the bias of the
error due to finite design and test samples is identical to the bias due to finite
design samples alone. Finite test samples do not contribute to the bias.
The variance of can be obtained from (5.98) as

-(I) -(2)
- 2PlP2Cov{a, ,ak } , (5.103)
where

1
1
-
- --- (E; - -)2 =E;(I -E;), (5.104)
4 2

-_
-Cl;ak . (5.105)
The second line of (5.104) can be derived from the first line as seen in (5.46).
From (5.109, a portion of (5.103) can be expressed as
-(2) -(2)
P:cov(a, ,ak I +P;Cov{a, ,aL I - ~P,P~cov{~, ,ar I
-(I)
-(I) -(I)
-(2)

e
= Var,{e) , (5.106)
where Vard{i) is the same one as (5.97). On the other hand, (5.105) can be
approximated as