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NONPARAMETRIC REGRESSION ON FUNCTIONAL DATA: INFERENCE AND PRACTICAL ASPECTS
Author(s) -
Ferraty Frédéric,
Mas André,
Vieu Philippe
Publication year - 2007
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2007.00480.x
Subject(s) - bootstrapping (finance) , nonparametric statistics , nonparametric regression , kernel (algebra) , inference , kernel regression , context (archaeology) , computer science , functional data analysis , mathematics , statistical inference , econometrics , statistics , artificial intelligence , paleontology , combinatorics , biology
Summary We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is tackled using a nonparametric kernel approach, which has been recently adapted to this functional context. We derive theoretical results from a deep asymptotic analysis of the behaviour of the estimate, including mean squared convergence (with rates and precise evaluation of the constant terms) as well as asymptotic distribution. Practical use of these results relies on the ability to estimate these constants. Some perspectives in this direction are discussed. In particular, a functional version of wild bootstrapping ideas is proposed and used both on simulated and real functional datasets.