B0718
Title: On the fitting of the distribution of the excess over a confidence level and the adaption for threshold detection
Authors: Daniel Gaigall - FH Aachen University of Applied Sciences (Germany) [presenting]
Julian Gerstenberg - Goethe University Frankfurt (Germany)
Abstract: The Cramer-von-Mises distance is applied to the distribution of the excess over a confidence level. Asymptotics of related statistics are investigated, and it is seen that the obtained limit distributions differ from the classical ones. For that reason, new bootstrap techniques for approximation purposes are introduced and justified. As an application, the consistency and the asymptotic exactness of a new goodness-of-fit test for the distribution of the excess over a confidence level are deduced. In addition, the results motivate a new confidence interval for the related fitting error. A practice-oriented usage is the determination of appropriate confidence levels for the fitting of the distribution of the excess over a confidence level, where limit results are derived. The adaption for the well-known problem of threshold detection is outlined and illustrated by a real-data example. Simulation studies investigate the quality of the new approximations.
