ROC Curves for Continuous Data

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“k10031final” — 2009/4/6 — 12:30 — page 42 — #50

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42 CHAPTER 3. ESTIMATION

N respectively, and if n

A(t)

denotes the number of individuals in the

sample from population A (where A is either N or P) whose classifica-

tion scores are greater than t, then the empirical estimators of the true

positive rate tp = p(S>t|P) and false positive rate fp = p(S>t|N) at

the classifier threshold t are given by



tp =

n

P (t)

n

P

,

and



fp =

n

N(t)

n

N

.

Thus plotting the set of values 1 −



fp against t yields the empirical

distribution function

ˆ

F (t), and doing the same for values 1 −



tp yields

the empirical distribution function

ˆ

G(t).

The empirical ROC curve is then simply given ...