Copula-based functional Bayes classification with principal components and partial least squares

We present a new functional Bayes classifier that uses principal component (PC) or partial least squares (PLS) scores from the common 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 by kernel smoothing and the copula is modeled parametrically. We focus on Gaussian and t-copulas, but other copulas could be used. The strong performance of our methodology is demonstrated through simulation, real data examples, and asymptotic properties.