Estimation of the misclassification probabilities for the linear discriminant function in high-dimensional case


3

Day & Time
31st July 2015, 15:00 ~
Venue
Room C816, Building of the Faculty of Science Graduate school of Science
Lecturer
Mr. Tomoyuki NAKAGAWA
(Ph. D. course student of Hiroshima University)
Presentation Title
Estimation of the misclassification probabilities for the linear discriminant function in high-dimensional case
Abstract
Cross validation(CV) and asymptotic expansions are known as the technique of estimating the misclassification probabilities. By using asymptotic expansions, we can correct higher order bias. However its technique depends on the distribution and the classifier. On the other hand, a method of CV does not depend on the distribution and the classifier. However, CV takes heavy costs of calculating. Moreover, theoretical approximation precision of CV is not clearly known in high-dimensional case.
We consider to use the linear discriminant function in a classification problem between two normal populations. Then, we investigate the bias and the MSE of the estimator by CV when both the sample size and the dimension are large. Moreover, we suggest that a method of correcting the bias of CV by using leave-2-out CV.