On properties of percentile bootstrap confidence intervals for prediction in functional linear regression

We consider a functional linear regression model with scalar response and functional covariate. For this model bootstrap confidence intervals for prediction using the residual resampling method have been already studied. In this paper, we use the paired resampling method to construct bootstrap confidence intervals for prediction in the functional linear regression model. We develop Edgeworth expansions for distribution of the prediction and apply the results to obtain coverage errors of percentile equal-tailed bootstrap confidence intervals for prediction. We carry out a simulation study to illustrate the numerical performance of the paired bootstrap confidence intervals and compare the results with those obtained by the residual resampling method.