On functional logistic regression via RKHS's
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In this work we address the problem of functional logistic regression, relying on the theory of RKHS's. The most common approach in the literature is to directly extend the multiple logistic model, replacing the inner product in R^d with the inner product in L^2[0,1]. In contrast, we propose to use the inner product of the RKHS associated with the process. It is a well-known fact that the Gaussian homoscedastic model for binary classification in R^d entails the logistic model. We analyze under which conditions L^2 and RKHS models hold. In this regard, the RKHS model can be seen as a generalization of the L^2 one, since it requires weaker conditions on the mean functions. In addition, this new approach is specially suitable to perform variable selection on the curves (in the sense that the finite-dimensional logistic model is a particular case). Besides, we carefully analyze whether the maximum likelihood estimators of both functional logistic models exist.
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