Classification accuracy measures with minimum error rate for normal mixture

정규혼합분포에서 최소오류의 분류정확도 측도

  • Hong, C.S. (Department of Statistics, Sungkyunkwan University) ;
  • Lin, Meihua (Research Institute of Applied Statistics, Sungkyunkwan University) ;
  • Hong, S.W. (Research Institute of Applied Statistics, Sungkyunkwan University) ;
  • Kim, G.C. (Research Institute of Applied Statistics, Sungkyunkwan University)
  • 홍종선 (성균관대학교 경제학부 통계학과) ;
  • ;
  • 홍선우 (성균관대학교 응용통계연구소, 통계학과) ;
  • 김강천 (성균관대학교 응용통계연구소, 통계학과)
  • Received : 2011.05.21
  • Accepted : 2011.06.20
  • Published : 2011.08.01

Abstract

In order to estimate an appropriate threshold and evaluate its performance for the data mixed with two different distributions, nine kinds of well-known classification accuracy measures such as MVD, Youden's index, the closest-to- (0,1) criterion, the amended closest-to- (0,1) criterion, SSS, symmetry point, accuracy area, TA, TR are clustered into five categories on the basis of their characters. In credit evaluation study, it is assumed that the score random variable follows normal mixture distributions of the default and non-default states. For various normal mixtures, optimal cut-off points for classification measures belong to each category are obtained and type I and II error rates corresponding to these cut-off points are calculated. Then we explore the cases when these error rates are minimized. If normal mixtures might be estimated for these kinds of real data, we could make use of results of this study to select the best classification accuracy measure which has the minimum error rate.

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