6 papers · 1 filter
Transferring supremum-norm rates and weak convergence of covariance kernel estimators to functional principal components
Hajo Holzmann, Kevin Wilk
We show that -perturbation theory can be used to transfer rates of convergence in the supremum norm as well as weak convergence in the space of continuous functions from covar…
Optimal rates for estimating the covariance kernel from synchronously sampled functional data
Max Berger, Hajo Holzmann
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which i…
Smooth and rough paths in mean derivative estimation for functional data
Max Berger, Hajo Holzmann
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional dat…
Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations
Hajo Holzmann, Alexander Meister
Expected values weighted by the inverse of a multivariate density or, equivalently, Lebesgue integrals of regression functions with multivariate regressors occur in various areas o…
Support estimation in high-dimensional heteroscedastic mean regression
Philipp Hermann, Hajo Holzmann
A current strand of research in high-dimensional statistics deals with robustifying the available methodology with respect to deviations from the pervasive light-tail assumptions.…
From dense to sparse design: Optimal rates under the supremum norm for estimating the mean function in functional data analysis
Max Berger, Philipp Hermann, Hajo Holzmann
We derive optimal rates of convergence in the supremum norm for estimating the Hölder-smooth mean function of a stochastic process which is repeatedly and discretely observed with…