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Testing model assumptions in functional regression models. (English) Zbl 1219.62075
Summary: In the functional regression model where the responses are curves, new tests for the functional form of the regression and the variance function are proposed, which are based on stochastic process estimating \(L^{2}\)-distances. Our approach avoids the explicit estimation of the functional regression and it is shown that normalized versions of the proposed test statistics converge weakly. The finite sample properties of the tests are illustrated by means of a small simulation study. It is also demonstrated that for small samples, bootstrap versions of the tests improve the quality of the approximation of the nominal level.

MSC:
62G10 Nonparametric hypothesis testing
62G08 Nonparametric regression and quantile regression
62M99 Inference from stochastic processes
65C60 Computational problems in statistics (MSC2010)
60F05 Central limit and other weak theorems
62F40 Bootstrap, jackknife and other resampling methods
Software:
fda (R); nlmdl
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References:
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