11 citations · 19 across the 12 of their papers we have counts for
16 papers
Tests of graph homogeneity, subgraph counts, and quasirandomness
Rudolf Grübel
Homogeneous random graphs, also known as Erd{\H os}-Rényi graphs, are a subset of the family of dense random graphs, specified by a graphon. We analyze several goodness-of-fit test…
Pattern-based tests for two-dimensional copulas
L. Baringhaus, R. Grübel
In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, t…
Efficiency of pattern-based independence test
L. Baringhaus, R. Grübel
Tests of independence are an important tool in applications, specifically in connection with the detection of a relationship between variables; they also have initiated many develo…
Discrete mixture representations of spherical distributions
Ludwig Baringhaus, Rudolf Grübel
We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises--Fisher, the Watson and the angular Gaus…
A note on limits of sequences of binary trees
Rudolf Grübel
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigat…
The quarter median
Ludwig Baringhaus, Rudolf Grübel
We introduce and discuss a multivariate version of the classical median that is based on an equipartition property with respect to quarter spaces. These arise as pairwise intersect…
Discrete mixture representations of parametric distribution families: geometry and statistics
Ludwig Baringhaus, Rudolf Grübel
We investigate existence and properties of discrete mixture representations for a given family , , of probability measures. The noncen…
Mixture representations of noncentral distributions
Ludwig Baringhaus, Rudolf Grübel
With any symmetric distribution on the real line we may associate a parametric family of noncentral distributions as the distributions of , , where is a r…
A boundary theory approach to de Finetti's theorem
Julian Gerstenberg, Rudolf Grübel, Klaas Hagemann
We show that boundary theory for transient Markov chains, as initiated by Doob, can be used to prove de Finetti's classical representation result for exchangeable random sequences.…
Edgeworth expansions for profiles of lattice branching random walks
Rudolf Grübel, Zakhar Kabluchko
Consider a branching random walk on in discrete time. Denote by the number of particles at site at time . By the profile of th…
Doob--Martin boundary of Rémy's tree growth chain
Steven N. Evans, Rudolf Grübel, Anton Wakolbinger
Rémy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the tree is uniformly distributed over the set of root…
A functional central limit theorem for branching random walks, almost sure weak convergence, and applications to random trees
Rudolf Grübel, Zakhar Kabluchko
Let be the limit of the Biggins martingale associated to a supercritical branching random walk with mean number of offspring . We prove a functional cen…
Persisting randomness in randomly growing discrete structures: graphs and search trees
Rudolf Grübel
The successive discrete structures generated by a sequential algorithm from random input constitute a Markov chain that may exhibit long term dependence on its first few input valu…
Random recursive trees: A boundary theory approach
Rudolf Grübel, Igor Michailow
We show that an algorithmic construction of sequences of recursive trees leads to a direct proof of the convergence of random recursive trees in an associated Doob-Martin compactif…
Search trees: Metric aspects and strong limit theorems
Rudolf Grübel
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on s…
Renewals for exponentially increasing lifetimes, with an application to digital search trees
Florian Dennert, Rudolf Grübel
We show that the number of renewals up to time exhibits distributional fluctuations as if the underlying lifetimes increase at an exponential rate in a distributio…