Title: Wavelet-Based Estimation of Generalized Discriminant Functions

Issue: Volume 81 Series B Part 2 Year 2019
Pages: 318 -- 349
In this work we propose a wavelet-based classifier method for binary classification. Basically, based on a training data set, we provide a classifier rule with minimum mean square error. Under mild assumptions, we present asymptotic results that provide the rates of convergence of our method compared to the Bayes classifier, ensuring universal consistency and strong universal consistency. Furthermore, in order to evaluate the performance of the proposed methodology for finite samples, we illustrate the approach using Monte Carlo simulations and real data set applications. The performance of the proposed methodology is compared with other classification methods widely used in the literature: support vector machine and logistic regression model. Numerical results showed a very competitive performance of the new wavelet-based classifier.
Primary: 62G05, 62G08, 62G20; Secondary:
Keywords and phrases: Generalized classification, wavelet estimation, nonparametric regression