
handle: 2078.1/116746
The functional nonparametric regression model \(Y=r(\chi)+\varepsilon\) is considered with a functional covariate \(\chi\) and a scalar response \(Y\). A kernel estimate \(\hat r\) is proposed for the regression operator \(r\). A bootstrap methodology is proposed allowing the construction of pointwise confidence intervals for \(r\). It is based on the residuals of \(\hat r\). Asymptotic consistency of the naive and wild bootstrap is demonstrated. Bandwidth selection for \(\hat r\) is discussed, and results of simulations are presented.
62G08 (62G09), wild bootstrap, kernel regression estimates, nonparametric regression, kernel estimator, naive bootstrap, Computational problems in statistics, Asymptotic normality, Nonparametric statistical resampling methods, Nonparametric regression and quantile regression, functional data, confidence intervals, bandwidth selection
62G08 (62G09), wild bootstrap, kernel regression estimates, nonparametric regression, kernel estimator, naive bootstrap, Computational problems in statistics, Asymptotic normality, Nonparametric statistical resampling methods, Nonparametric regression and quantile regression, functional data, confidence intervals, bandwidth selection
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