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Bootstrap in functional linear regression. (English) Zbl 1197.62068
Summary: We have considered a functional linear model with scalar response and functional explanatory variable. One of the most popular methodologies for estimating the model parameters is based on functional principal components analysis (FPCA). In recent literature, weak convergence for a wide class of FPCA-type estimates has been proved, and consequently asymptotic confidence sets can be built. We have proposed an alternative approach in order to obtain pointwise confidence intervals by means of a bootstrap procedure, for which we have obtained its asymptotic validity. Besides, a simulation study allows us to compare the practical behaviour of asymptotic and bootstrap confidence intervals in terms of coverage rates for different sample sizes.

MSC:
62H25 Factor analysis and principal components; correspondence analysis
62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62F40 Bootstrap, jackknife and other resampling methods
Software:
fda (R)
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References:
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