This paper is concerned with the distributions used to construct confidence intervals for the regression function in a nonparametric setup. The rates of convergence for the normal limit, its plug in approach and the wild bootstrap are compared conditionally on the explanatory variable X and also...

From noisy observations of a finite family of functions an approximation in a lower dimensional space can be constructed using the method of principal components. If certain restrictions are to be satisfied by the approximation, e.g. being densities, this leads to a modified estimation...