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Further Results in Estimating the Classification Error in Discriminance Analysis
Author(s) -
Wernecke K.D.,
Kalb G.
Publication year - 1983
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.19830250305
Subject(s) - statistics , weighting , sample size determination , mathematics , skewness , sample (material) , covariance , sample variance , population , truncation (statistics) , estimation , computer science , variance (accounting) , medicine , chemistry , demography , management , chromatography , sociology , economics , radiology , accounting , business
Basing on the approach by McLachlan (1977) a procedure for the conditional and common error estimation of the classification error in discriminance analysis is described for k ≧ 2 classes. As a rapid procedure for large sample sizes and feature numbers, a modification of the resubstitution method is proposed being favourable with respect to computing time. Both methods provide useful estimations for the probability of misclassification. In calculating the weighting function w , deviations from preconditions known from the MANOVA such as the skewness, the truncation or the inequality of the covariance matrices, hardly play any role; it appears that only a variation of the sample sizes of the classes substantially influences the weighting functions. The error rates of the tested error estimation methods likewise in effect depend on the sample sizes of the classes. Violations of the mentioned preconditions in the form described above result in different variations of the error estimates, depending on these sample sizes. A comparison between error estimation and allocation relative to a simulated population demonstrates the goodness of the used error estimation procedures.