An estimator of misclassification probability for multi-class Euclidean distance classifier in high-dimensional data

Source abstract

Aoshima and Yata [1] observed that classification accuracy of Euclidean distance-based classifiers have good performance at high dimensions. For practical use, it is necessary to estimate the misclassification probability using the training data set. Although cross-validation is usually used for such problems, it does not necessarily have good estimation accuracy at high dimension. In this paper, we propose a new estimator of misclassification probabilities at high-dimensional settings. Our estimator is obtained using the asymptotic multivariate normality of discriminant functions at high-dimensional settings. Finally, we numerically justify the high accuracy of our proposed estimator in finite sample applications, inclusive of high-dimensional scenarios.