Optimal Bayes Classifiers for Functional Data and Density Ratios

• Activity Number: 262
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xiongtao Dai* and Hans-Georg G. Mueller and Fang Yao
• Companies: and UC Davis and University of Toronto
• Keywords: functional classification ; Bayes classifier ; common functional principal components ; Gaussian process

Abstract

When constructing Bayes classifiers for functional data, one encounters the problem that probability density functions do not exist for these data due to the low small ball probabilities. As a consequence the classical Bayes classifier using density quotients needs to be modified. We construct Bayes classifiers by using density ratios of projections on a sequence of eigenfunctions that are common to the groups to be classified and study their asymptotic behavior. In the large sample limit, our classifiers achieve perfect classification under certain conditions and they also behave favorably compared to other classifiers in simulations and in various well-studied classification problems with functional predictors.