Bachelor- or Master Thesis „Monte-Carlo tests based on functionals of Gaussian processes"
Many statistical processes of interest (as , e.g., empirical processes, Aalen Johansen processes,...) converge in distribution to a Gaussian limit and corresponding asymptotically valid tests (e.g. goodness of fit tests) or confidence bands (e.g. for cumulative incidences) are derived from functionals (as, e.g., supremum or integral functionals) thereof. If, however, the limit functional of the Gaussian process depends on unknown quantitities, approximation technques are needed for calculating critical values. Here, one simpe possibility would be to apply a Monte Carlo test based on simulating the Gaussian limit process with estimated covariance function. After introducing the corresponding theory the resulting procedures should be compared with resampling based techniques (as, e.g., the bootstrap) in an extensive simulation study.
This thesis will be supervised jointly by the Institutes of Statistics and Stochastics.
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