The asymptotic efror rate of the equal-mean, uniform-covariance-matrix classification rule is approximated by a first order asymptotic expansion. The approximation is compared for accuracy with a Monte Carlo simulation. Finally, an estimator of the error rate and an estimator of the variance of the error rate eatimator are derived and applied to a classical example.
Srivastava (1980) has shown that Grubbs's (1950) test for a univariate outlier is robust against the effect of equicorrelation. In this note we extend Srivastava's result by giving a more general covariance structure, which relaxes both the covariance structure and the assumption of equal variances. We also show that under the more general covariance structure, the power of Gmbbs's test, as well as the significance level, is identical to the independently and identically distributed case. RESUME Srivastava (1980) a rnontri que le test de Grubbs (1950) pour ditecter une observation aberrante univarite est robuste contre l'effet de l'tquicorrilation. On gtntralise ici le rtsultat de Srivastava en considkrant des hypothbes moins restrictives sur la structure de covariance et en ne supposant plus I'kgalitt des variances. On montre aussi que, sous nos hypothhses, la puissance du test de Grubb, ainsi que le niveau de signification, restent les m h e s que dans le cas de variables indkpendantes et identiquernent distributes.
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.
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