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Title: Functional logistic regression: An RKHS approach Authors:  Jose Berrendero - Universidad Autonoma de Madrid (Spain) [presenting]
Beatriz Bueno-Larraz - Universidad Autonoma de Madrid (Spain)
Antonio Cuevas - Autonomous University of Madrid (Spain)
Abstract: A functional logistic regression model is proposed to explore the relationship between a dichotomous response variable and a functional predictor. The proposal is based on ideas borrowed from the theory of reproducing kernel Hilbert spaces (RKHS). Similarly to the finite-dimensional case, our model holds when the conditional distributions of the predictor given the two possible values of the response are Gaussian with the same covariance structure. Moreover, some particular choices of the slope function lead to the point-impact model. We also give conditions (which include Brownian-like predictors) under which the maximum likelihood estimator of the slope function does not exist with probability one and address some possible solutions.