Asymptotic Evaluation of the Probabilities of Misclassification by Linear Discriminant Functions
STANFORD UNIV CA DEPT OF STATISTICS
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Linear discriminant functions are used to classify an observation as coming from one of two normal populations with common covariance matrices and different means when samples are used to estimate the parameters of the distributions. Okamotos asymptotic expansion of the distribution of the classification statistic W is compared with Andersons expansion for the Studentized W that is, W standardized by estimates of its mean and standard deviation. Some numerical evaluations of the term of order of the reciprocal of the sample sizes is given. The uses of the two approximate distributions are discussed.
- Statistics and Probability