A0296
Title: Fourier approach to goodness-of-fit tests for Gaussian random processes
Authors: Daniel Hlubinka - Univerzita Karlova (Czech Republic) [presenting]
Zdenek Hlavka - Charles University (Czech Republic)
Petr Coupek - Charles University (Czech Republic)
Viktor Dolnik - Charles University (Czech Republic)
Abstract: A new goodness-of-fit (GoF) test is proposed and investigated for the Gaussianity of the observed functional data. The test statistic is the Cramr-von Mises distance between the observed empirical characteristic functional (CF) and the theoretical CFcorresponding to the null hypothesis stating that the functional observations (process paths) were generated from a specific parametric family of Gaussian processes, possibly with unknown parameters. The asymptotic null distribution of the proposed test statistic is also derived in the presence of these nuisance parameters, the consistency of the classical parametric bootstrap is established, and some particular choices of the necessary tuning parameters are discussed. The empirical level and power are investigated in a simulation study involving GoF tests of an Ornstein-Uhlenbeck process, Vasicek model, or a (fractional) Brownian motion, both with and without nuisance parameters, with suitable Gaussian and non-Gaussian alternatives.
