Score-type statistics in pattern classification

Abstract

Statistical classification methods based on score statistics have received a considerable attention in recent years. The use of these methodologies requires that asymptotic properties relative to such measures are satisfied. In this context, the classification error rates generally present biased values to the nominal level when submitted to small or moderate sample sizes. However, Nelson, Turin and Hastie [Journal of Pattern Recognition and Artificial Intelligence 8 (1994) 749–770] proposed a successful classification method based on score statistic described asymptotically by a chi-square law. That proposal presented good results for several sample sizes. On the other hand, stochastic measures with exact distributions described by beta and Hotelling’s $\mathcal{T}^{2}$ laws have also been employed in such situations. This paper presents two Bartlett-type corrections for score statistics considering the method proposed by Cordeiro and Ferrari [J. Statist. Plann. Inference 71 (1998) 261–269]. Moreover, Monte Carlo experiments are performed in order to compare the corrected statistics to their respective noncorrected versions and to a classic classifier defined on the nonmodified score statistic. In a confirmatory sense, the proposed methodology is applied to actual signature data, obtained by the Electrical Engineering and Computer Department from the State University of Campinas (UNICAMP, Brazil).