Least Squares and Shrinkage Estimation under Bimonotonicity Constraints (2008)
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 bimonotone r-by-s matrices....
On an Auxiliary Function for Log-Density Estimation (2008)
Cule, Madeleine L., Duembgen, Lutz
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 a log-linear...
Nemirovski's Inequalities Revisited (2008)
Duembgen, Lutz, Van De Geer, Sara, Wellner, Jon A.
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 inequalities: For...
Extensions of Smoothing via Taut Strings (2008)
Suppose that we observe independent random pairs (X_1,Y_1), (X_2,Y_2), ..., (X_n,Y_n).Our goal is to estimate regression functions such as the conditional mean or beta-quantile of Y given X, where 0...
Rohde, Angelika, Duembgen, Lutz
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures...
P-values for classification (2008)
Duembgen, Lutz, Igl, Bernd-Wolfgang, Munk, Axel
Let $(X,Y)$ be a random variable consisting of an observed feature vector $X\in \mathcal{X}$ and an unobserved class label $Y\in \{1,2,...,L\}$ with unknown joint distribution. In addition, let...
Duembgen, Lutz, Rufibach, Kaspar
We study nonparametric maximum likelihood estimation of a log--concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two...
Multiscale inference about a density (2007)
Duembgen, Lutz, Walther, Günther
We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases...
Explicit bounds for the approximation error in Benford's law (2007)
Duembgen, Lutz, Leuenberger, Christoph
Benford's law states that for many random variables X > 0 its leading digit D = D(X) satisfies approximately the equation P(D = d) = log_{10}(1 + 1/d) for d = 1,2,...,9. This phenomenon follows from...
Marshall's lemma for convex density estimation (2006)
Duembgen, Lutz, Rufibach, Kaspar, Wellner, Jon A.
Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies $\sqrt{n}$--consistency of the distribution function corresponding to the...
Confidence bands for convex median curves using sign-tests (2006)
Suppose that one observes pairs $(x_1,Y_1)$, $(x_2,Y_2)$, ..., $(x_n,Y_n)$, where $x_1\le x_2\le ... \le x_n$ are fixed numbers, and $Y_1,Y_2,...,Y_n$ are independent random variables with unknown...