7.7 Fishers Classification Procedure Based of On Sample Discriminate

Allocate \(X\) to \(\pi _k\) if \begin {align*} \sum ^r_{j=1}\big (\widehat {Y}_j-\overline {Y}_{kj}\big )^2 & = \sum ^r_{j=1}\big [\widehat {L}'_j\big (X-\overline {X}\big )\big ]^2\\ & = \sum ^r_{j=1}\big [\widehat {e}'_j\big (X-\overline {X}_j\big )\big ]^2\qquad \text {for all}\quad j\neq k\\ \end {align*}