%0 Journal Article
%@ 0090-5364
%A Dümbgen, Lutz
%C Hayward, Calif.
%D 1998
%F heidok:20896
%I IMS Business Office
%J The Annals of Statistics
%K Adaptivity; conditional median; convexity; distribution-free; interval censoring; modality; monotonicity; signs of residuals; spacings
%N 1
%P 288-314
%R 10.11588/heidok.00020896
%T New Goodness-of-Fit Tests and their Application toNonparametric Confidence Sets
%U https://archiv.ub.uni-heidelberg.de/volltextserver/20896/
%V 26
%X Suppose one observes a process V on the unit interval, wheredV(t) = f(t) + dW(t) with an unknown function f and standard Brownian motion W. We propose a particular test of one-point hypotheses about f which is based on suitably standardized increments of V.This test is shown to have desirable consistency properties if, for instance, fis restricted to various Hölder smoothness classes of functions. Thetest is mimicked in the context of nonparametric density estimation,nonparametric regression and interval censored data. Under shaperestrictions on the parameter f such as monotonicity or convexity, weobtain confidence sets for f adapting to its unknown smoothness.