Linear functional regression: The case of fixed design and functional response.

*(English)*Zbl 1012.62039Summary: The authors consider the problem of simple linear regression when the exogeneous and endogenous variables are functional and the design is fixed. They propose an estimator for the underlying linear operator and prove its consistency under some conditions which ensure that the design is sufficiently informative. They consider the classical calibration (or inverse regression) problem and analyze a consistent estimator. They also give a simulation study. The proposed method is not hard to implement in practice.

##### MSC:

62G08 | Nonparametric regression and quantile regression |

62J05 | Linear regression; mixed models |

62J02 | General nonlinear regression |

##### Keywords:

calibration; consistent estimation; functional data; functional regression; linear operators; Yurinskii’s inequality##### Software:

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\textit{A. Cuevas} et al., Can. J. Stat. 30, No. 2, 285--300 (2002; Zbl 1012.62039)

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