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Multilayer perceptron with functional inputs: an inverse regression approach. (English) Zbl 1164.62339

A functional sliced inverse regression (FSIR) technique is considered for fitting the model

Y=f(X,a 1 ,,X,a p ,ε),

where Y is the response, X is a functional regressor (a random function in L 2 [a,b]), f is an unknown regression function, a 1 are unknown functions, and ε is an error term. Consistency of regularized FSIR estimates for a i is demonstrated. It is proposed to estimate the function f by a multilayer perceptron technique. Consistency of the proposed training algorithm for such perceptrons is shown. Applications to real data are considered.

MSC:
62G08Nonparametric regression
62G20Nonparametric asymptotic efficiency
62G99Nonparametric inference
62J12Generalized linear models
Software:
fda (R)