Nonparametric functional data analysis is a field whose development started some 15 years ago and there is a very extensive literature on the topic (hundreds of papers published now). The first aim of this survey is to discuss the state of art in the field through a necessarily selected, bibliographical survey. The second aim is to present a wide scope of open questions in order to promote further discussions. Our main purpose is restricted to methodological contributions and also to emphasize on kernel functional regression analysis before extending discussions in two directions: alternative techniques to kernel methods for functional regression and other statistical problems besides regression.
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Ling et al. (2018) studied this question.
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