4 papers
Limiting properties of monotone rearrangements of estimators when the truth is flat
Holger Dette, Marius Kroll, Stanislav Volgushev
Monotone rearrangements provide a simple way to enforce shape constraints of an estimator, but existing distributional theory does not cover flat regions, where the target induces…
Detecting practically significant dependencies in metric spaces via distance correlations
Holger Dette, Marius Kroll
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance c…
Extension of Process Convergence With Application to Chatterjee's Rank Correlation
Marius Kroll
We give conditions under which weak convergence of a stochastic process indexed in the class of -dimensional hyperrectangles is sufficient to ensure convergence in the larger cl…
Asymptotic Normality of -Statistics is Equivalent to Convergence in the Wasserstein Distance
Marius Kroll
We prove the claim in the title under mild conditions which are usually satisfied when trying to establish asymptotic normality. We assume strictly stationary and absolutely regula…