Abstract: We present a new functional Bayes classifier that uses principal component (PC) or partial least squares (PLS) scores from the common (i.e. pooled) covariance function, that is, the covariance function marginalized over groups. When the groups have different covariance functions, the PC or PLS scores need not be independent or even uncorrelated. We use copulas to model the dependence. Our method is semiparametric; the marginal densities are estimated nonparametrically using kernel smoothing, and the copula is modeled parametrically. We focus on Gaussian and t-copulas, but other copulas can be used. The strong performance of our methodology is demonstrated through simulation, real-data examples, and asymptotic properties.

Key words and phrases: Asymptotic theory, Bayes classifier, functional data, perfect classification, rank correlation, semiparametric model.