93 citations · 173 across the 3 of their papers we have counts for
5 papers
Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry
Wanli Qiao, Wolfgang Polonik
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizont…
Multiscale geometric feature extraction for high-dimensional and non-Euclidean data with application
Gabriel Chandler, Wolfgang Polonik
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature funct…
On the choice of weight functions for linear representations of persistence diagrams
Vincent Divol, Wolfgang Polonik
Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly…
Asymptotic normality of plug-in level set estimates
David M. Mason, Wolfgang Polonik
We establish the asymptotic normality of the -measure of the symmetric difference between the level set and a plug-in-type estimator of it formed by replacing the density in the…
Empirical spectral processes for locally stationary time series
Rainer Dahlhaus, Wolfgang Polonik
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a…