Page 199 - Introduction to Statistical Pattern Recognition

Chapter 5

PARAMETER ESTIMATION

As discussed in the previous chapters, once we express the density func-
tions in terms of parameters such as expected vectors and covariance matrices,
we can design the likelihood ratio classifier to partition the space. Another
alternative is to express the discriminant function in terms of a number of
parameters, assuming a mathematical form such as a linear or quadratic func-
tion. Even in this case, the discriminant function often becomes a function of
expected vectors and covariance matrices, as seen in Chapter 4. In either case,
we call it the parametric approach. The parametric approach is generally con-
sidered less complicated than its counterpart, the nonparametric approach, in
which mathematical structures are not imposed on either the density functions
or the discriminant function.

In the previous chapters, we have assumed that the values of the parame-
ters are given and fixed. Unfortunately, in practice their true values are never
known, and must be estimated from a finite number of available samples. This
is done by using the sample estimation technique presented in Section 2.2.
However, the estimates are random variables and vary around the expected
values.
The statistical properties of sample estimates may be obtained easily as
discussed in Section 2.2. However, in pattern recognition, we deal with func-
tions of these estimates such as the discriminant function, the density function,

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