Functional canonical analysis for square integrable stochastic processes
Journal of Multivariate Analysis
Discriminant analysis for locally stationary processes
Journal of Multivariate Analysis
Estimation in generalized linear models for functional data via penalized likelihood
Journal of Multivariate Analysis
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Functional classification in Hilbert spaces
IEEE Transactions on Information Theory
On local times, density estimation and supervised classification from functional data
Journal of Multivariate Analysis
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In this paper we present a general notion of Fisher's linear discriminant analysis that extends the classical multivariate concept to situations that allow for function-valued random elements. The development uses a bijective mapping that connects a second order process to the reproducing kernel Hilbert space generated by its within class covariance kernel. This approach provides a seamless transition between Fisher's original development and infinite dimensional settings that lends itself well to computation via smoothing and regularization. Simulation results and real data examples are provided to illustrate the methodology.