B1376
Title: A consistent goodness-of-fit test in separable Hilbert spaces with applications to high dimensional data
Authors: Daniel Gaigall - FH Aachen University of Applied Sciences (Germany) [presenting]
Marc Ditzhaus - Otto-von-Guericke University Magdeburg (Germany)
Abstract: A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is considered. The test statistic based on the Cramer-von-Mises statistic applied to projected data and is given by an integral over the projections. Applications include functional data in $\mathcal L^2$-spaces or observations in $\mathbb R^d$, where the dimension $d$ may be fixed or it may depend on the sample size $n$, i.e. $d=d_n$ and $d_n\to\infty$ as $n\to\infty$. The convergence in distribution of the test statistic under the null hypothesis is shown and the consistency of the test is concluded.
Journal