77 citations · 240 across the 21 of their papers we have counts for
22 papers
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…
Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures
Johanna Ziegel, David Ginsbourger, Lutz Dümbgen
We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernel…
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…
New Algorithms for -Estimation of Multivariate Scatter and Location
Lutz Duembgen, Klaus Nordhausen, Heike Schuhmacher
We present new algorithms for -estimators of multivariate scatter and location and for symmetrized -estimators of multivariate scatter. The new algorithms are considerably fa…
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…
Maximum-Likelihood Estimation of a Log-Concave Density based on Censored Data
Lutz Duembgen, Kaspar Rufibach, Dominic Schuhmacher
We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a sub…
Inference on a Distribution Function from Ranked Set Samples
Lutz Duembgen, Ehsan Zamanzade
Consider independent observations , , \ldots, with random or fixed ranks , while conditional on , the random va…
(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…
Stochastic Search for Semiparametric Linear Regression Models
Lutz Duembgen, Dominic Schuhmacher, Richard Samworth
This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar (1987). The idea is to generate…
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…
Multivariate Log-Concave Distributions as a Nearly Parametric Model
Dominic Schuhmacher, Andre Huesler, Lutz Duembgen
In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that w…
Least Squares and Shrinkage Estimation under Bimonotonicity Constraints
Rudolf Beran, Lutz Duembgen
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonoto…
On an Auxiliary Function for Log-Density Estimation
Madeleine L. Cule, Lutz Duembgen
In this note we provide explicit expressions and expansions for a special function which appears in nonparametric estimation of log-densities. This function returns the integral of…
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…