Some Results on Error Rates for Quadratic Discrimination with Known Population Parameters

Abstract

Let populationZIi, i = 1,2, be characterized by a multivariate normal density function, N ( p i , Z i ) , i = 1.2, respectively. This paper providee conditions under which simple conditional error rates may be computed for the quadratic discriminant function with known population parametera. Alao, a simple bound on the overall e'rror rate is derived. Examplea are given which demonstrate the proposed methods.

Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions. I. The Equal-Means Case

“…Bartlett and Please [2], Desu and Geisser [4], Young et al [21], and Marco et al [10]) provided additional analyses of Stocks' data. These authors chose random samples of 30 monozygotic and 30 dizygotic twins such that there were 15 female twins and 15 male twins in each group, based on the following subset of 10 variables from Stocks' original 14 variables: As in [16], for each group of twins the difference between the first and second twin is taken as the observation, and the common mean of each population is assumed to be the zero vector.…”

“…Bartlett and Please [2], under the assumption of the uniform covariance structure given in (1.12) where all parameters are assumed to be known, estimated an upper bound for the TPMC; Marco et al [10], working with the same uniform covariance structure assumption, but with all the parameters unknown, obtained an asymptotic estimate of the TPMC; Young et al [21], with no covariance restrictions but with all parameters are assumed known, estimated an upper bound for the TPMC; all these authors utilized an analog of Q 2 . We also applied the asymptotic approximations of Okamoto [16] Recall that we modified Stocks' data set, reducing the number of variables from ten to seven, because the biplot in Fig.…”