Variable informativeness in discriminant analysis

Tatjana Pavlenko

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998

ISSN 0281-1944
ISRN LUNFD6/NFMS--3194--SE


Abstract:
The performance of discrimination, measured by overall conditional error rate, is effected by variable informativeness. Our point is to evaluate this effect in an asymptotic setup. We suggest to regard the informativeness of a set of variables as a random value with a proper distribution. In order to carry out the effect of informativeness on discrimination we introduce the weighted discriminant function. New asymptotic results for the error rate yielded by the weighted discriminant function are obtained in a sequence of discrimination problems. The optimal type of the weight function for which the overall conditional error rate achieves the minimum value is found.

Key words:
discrimination problem, growing dimension asymptotics, weighted discriminant function, conditional error rate