Estimation of misclassification probability for a distance-based classifier in high-dimensional data

The Euclidean distance-based classifier is often used to classify an observation into one of several populations in high-dimensional data. One of the most important problems in discriminant analysis is estimating the probability of misclassification. In this paper, we propose a consistent estimator of misclassification probabilities when the dimension of the vector, p, may exceed the sample size, N , and the underlying distribution need not necessarily be normal. A new estimator of quadratic form is also obtained as a by-product. Finally, we numerically verify the high accuracy of our proposed estimator in finite sample applications, inclusive of high-dimensional scenarios. AMS 2000 subject classification: 62H30, 41A60.