Page 110 - Introduction to Statistical Pattern Recognition

92 Introduction to Statistical Pattern Recognition

(3.127)

where yi. vi, and hi are the components of Y, V, and A respectively. Depend-
ing on whether the error is generated by h(X) > 0 or h(X) < 0, the error must
be computed as

&T= { (3.128)

The integration of (3.128) must be carried out numerically. This integration is
not simple but is possible, because it is one-dimensional.
The result of (3.128) is quite general, because we may select the test dis-
tribution independently of the parameters used for design [15]. However, the
cases most frequently encountered in practice are MT = Mi and ZT = Xi
(2=1,2). Therefore, let us find vi. hi, and c for these cases.

MT = MI and ZT = 21: this case, we apply simultaneous diagonali-
In
zation and a coordinate shift such that