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Quadratic discriminant analysis (QDA) is a simple method to classify asubject into two populations, and was proven to perform as well as the Bayesrule when the data dimension p is fixed. The main purpose of this paper is toexamine the empirical and theoretical behaviors of QDA where p growsproportionally to the sample sizes without imposing any structural assumptionon the parameters. The first finding in this moderate dimension regime is thatQDA can perform as poorly as random guessing even when the two populationsdeviate significantly. This motivates a generalized version of QDA thatautomatically adapts to dimensionality. Under a finite fourth moment condition,we derive misclassification rates for both the generalized QDA and the optimalone. A direct comparison reveals one "easy" case where the difference betweentwo rates converges to zero and one "hard" case where that converges to somestrictly positive constant. For the latter, a divide-and-conquer approach overdimension (rather than sample) followed by a screening procedure is proposed tonarrow the gap. Various numerical studies are conducted to back up the proposedmethodology.

Quadratic Discriminant Analysis under Moderate Dimension