TY  - JOUR
A1  - Dümbgen, Lutz
CY  - Hayward, Calif.
TI  - New Goodness-of-Fit Tests and their Application toNonparametric Confidence Sets
ID  - heidok20896
JF  - The Annals of Statistics
SN  - 0090-5364
KW  - Adaptivity; conditional median; convexity; distribution-free; interval censoring; modality; monotonicity; signs of residuals; spacings
Y1  - 1998///
SP  - 288
PB  - IMS Business Office
IS  - 1
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/20896/
AV  - public
N2  - 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.
VL  - 26
EP  - 314
ER  -