A First Course in Multivariate Statistics pp 453-562 | Cite as

# Discrimination and Classification, Round 2

Chapter

## Abstract

In this chapter we continue the theory of classification developed in Chapter 5 on a somewhat more general level. We start out with some basic consideration of optimality. In the notation introduced in Section 5.4, will be referred to as *pdf*of*pdf*of

**Y**will denote a*p*-variate random vector measured in*k*groups (or populations). Let*X*denote a discrete random variable that indicates group membership, i.e., takes values 1, … ,*k*. The probabilities$$
{\pi _j} = \Pr \left[ {X = j} \right]\quad j = 1, \ldots ,k,
$$

(1)

*prior probabilities*, as usual. Suppose that the distribution of**Y**in the*j*th group is given by a*pdf f*_{ j }(**y**), which may be regarded as the conditional**Y**, given*X = j*. Assume for simplicity that*Y*is continuous with sample space ℝ^{ p }in each group. Then the joint*X*and**Y**, as seen from Sec tion 2.8, is$$
{f_{XY}}\left( {j,y} \right) = \left\{ \begin{gathered} {\pi _j}{f_j}\left( y \right)\;for{\kern 1pt} j = 1, \ldots ,k,y \in {\mathbb{R}^p} \hfill \\ 0\quad otherwise. \hfill \\ \end{gathered} \right.
$$

(2)

## Keywords

Covariance Matrice Canonical Variate Classification Rule Classification Region Standard Distance
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Suggested Further Reading

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