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In this paper, we generalize two criteria, the determinant-based andtrace-based criteria proposed by Saranadasa (1993), to general populations forhigh dimensional classification. These two criteria compare some distancesbetween a new observation and several different known groups. Thedeterminant-based criterion performs well for correlated variables byintegrating the covariance structure and is competitive to many other existingrules. The criterion however requires the measurement dimension be smaller thanthe sample size. The trace-based criterion in contrast, is an independence ruleand effective in the "large dimension-small sample size" scenario. An appealingproperty of these two criteria is that their implementation is straightforwardand there is no need for preliminary variable selection or use of turningparameters. Their asymptotic misclassification probabilities are derived usingthe theory of large dimensional random matrices. Their competitive performancesare illustrated by intensive Monte Carlo experiments and a real data analysis.

On Two Simple and Effective Procedures for High Dimensional Classification of General Populations