Title: Bootstrap confidence intervals in semi-functional partial linear regression under dependence
Authors: Paula Rana Miguez - Universidade da Coruna (Spain) [presenting]
German Aneiros-Perez - University of Coruna (Spain)
Juan Vilar Fernandez - Universidade da Coruna (Spain)
Philippe Vieu - University Paul Sabatier (France)
Abstract: Two bootstrap procedures, naive and wild bootstrap, are proposed to construct pointwise confidence intervals for the semi-functional partial lineal regression model, when the response is scalar and considering scalar covariates (for the linear component) and functional covariates (for the nonparametric component). By means of these two bootstrap procedures, we can approximate the asymptotic distribution for both parts in the model: the linear and the nonparametric components. The validity of the two bootstrap procedures has been proved theoretically in the setting of dependent data, assuming alpha-mixing conditions on the sample, and also for independent data as a particular case. Naive bootstrap allows dealing with homoscedastic data, meanwhile wild bootstrap is devoted to work with heteroscedastic data. Pointwise confidence intervals for each component of the model have been built. A simulation study shows the performance of the procedure, which has been also applied to a real dataset. Specifically, an application to electricity price from the Spanish Electricity Market illustrates its usefulness in practice.