A0968
Title: Quantitative inference about the variation of a function
Authors: Fabian Mies - Delft University of Technology (Netherlands) [presenting]
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Abstract: When performing nonparametric inference about a regression function, quantitative assessments are usually either point estimates, pointwise confidence intervals, or simultaneous confidence bands. While this gives some impression of the shape of the signal, it does not directly yield statistical statements about the variability of the function within the band. The aim is to quantify the variation of a function in terms of (a) its range, and (b) its total variation. Based on multiscale test statistics, simultaneous confidence intervals are constructed for these variation measures, as well as for the modulus of continuity of the regression function. For the special case of step functions, the methods yield novel multiscale tests for relevant changepoints.
