77 citations · 240 across the 21 of their papers we have counts for
14 papers · 1 filter
Approximating Symmetrized Estimators of Scatter via Balanced Incomplete U-Statistics
Lutz Duembgen, Klaus Nordhausen
We derive limiting distributions of symmetrized estimators of scatter, where instead of all pairs of the observations we only consider suitably chosen pairs, $1…
Honest calibration assessment for binary outcome predictions
Timo Dimitriadis, Lutz Duembgen, Alexander Henzi +2
Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability , it should materialize wi…
Various New Inequalities for Beta Distributions
Alexander Henzi, Lutz Duembgen
This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian…
Estimation of a Likelihood Ratio Ordered Family of Distributions
Alexandre Mösching, Lutz Duembgen
Consider bivariate observations with unknown conditional distributions of , given that . The goal is…
Bounding distributional errors via density ratios
Lutz Duembgen, Richard Samworth, Jon Wellner
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution to…
Connecting model-based and model-free approaches to linear least squares regression
Lutz Duembgen, Laurie Davies
In a regression setting with a response vector and given regressor vectors, a typical question is to what extent the response is related to these regressors, specifically, how well…
A law of the iterated logarithm for Grenander's estimator
Lutz Duembgen, Jon A. Wellner, Malcolm Wolff
In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If , , and is continuo…
A New Approach to Tests and Confidence Bands for Distribution Functions
Lutz Duembgen, Jon A. Wellner
We introduce new goodness-of-fit tests and corresponding confidence bands for distribution functions. They are inspired by multi-scale methods of testing and based on refined laws…
M-Functionals of Multivariate Scatter
Lutz Duembgen, Markus Pauly, Thomas Schweizer
This survey provides a self-contained account of -estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying -functionals and di…
(Ab)Using Regression for Data Adjustment
Lutz Duembgen
In various economic applications, people want to compare units with respect to certain quantities measuring their performance. The latter, however, is o…
On Low-Dimensional Projections of High-Dimensional Distributions
Lutz Duembgen, Perla Zerial
Let be a probability distribution on -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension , most -dimensional projections o…
Approximation by log-concave distributions, with applications to regression
Lutz Duembgen, Richard Samworth, Dominic Schuhmacher
We study the approximation of arbitrary distributions on -dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-typ…
Nemirovski's Inequalities Revisited
Lutz Duembgen, Sara van de Geer, Mark Veraar +1
An important tool for statistical research are moment inequalities for sums of independent random vectors. Nemirovski and coworkers (1983, 2000) derived one particular type of such…
Marshall's lemma for convex density estimation
Lutz Duembgen, Kaspar Rufibach, Jon A. Wellner
Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies --consistency of the distribution function corr…