Publications (33)
Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images
Bruno Ebner, Norbert Henze, Michael A. Klatt +1
We propose a class of goodness-of-fit tests for complete spatial randomness (CSR). In contrast to standard tests, our procedure utilizes a transformation of the data to a binary im…
A new flexible class of kernel-based tests of independence
Marija CupariÄ, Bruno Ebner, Bojana MiloÅ¡eviÄ
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. I…
A new omnibus test of fit based on a characterisation of the uniform distribution
Bruno Ebner, Shawn Liebenberg, Jaco Visagie
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distrib…
On a new test of fit to the beta distribution
Bruno Ebner, Shawn C. Liebenberg
We propose a new -type goodness-of-fit test for the family of beta distributions based on a conditional moment characterisation. The asymptotic null distribution is identified…
A goodness-of-fit test for the Zeta distribution with unknown parameter
Bruno Ebner, Daniel Hlubinka
We introduce a new goodness-of-fit test for count data on for the Zeta distribution with unknown parameter. The test is built on a Stein-type characterization that use…
Independent additive weighted bias distributions and associated goodness-of-fit tests
Bruno Ebner, Yvik Swan
We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related -type disc…
Testing normality via a distributional fixed point property in the Stein characterization
Steffen Betsch, Bruno Ebner
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on -distances of the empirical zero-bias trans…
Bahadur efficiencies of the Epps--Pulley test for normality
Bruno Ebner, Norbert Henze
The test for normality suggested by Epps and Pulley (1983) is a serious competitor to tests based on the empirical distribution function. In contrast to the latter procedures, it h…
The test of exponentiality based on the mean residual life function revisited
Bruno Ebner
We revisit the family of goodness-of-fit tests for exponentiality based on the mean residual life time proposed by Baringhaus & Henze (2008). We motivate the test statistic by a ch…
Testing multivariate uniformity based on random geometric graphs
Bruno Ebner, Franz Nestmann, Matthias Schulte
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set based on statistics related to edge lengths of random geometric graphs. Asym…
Stein's Method Meets Computational Statistics: A Review of Some Recent Developments
Andreas Anastasiou, Alessandro Barp, François-Xavier Briol +11
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin…
On Stein's test of uniformity on the hypersphere
Paul Axmann, Bruno Ebner, Eduardo GarcÃa-Portugués
We propose a new test of uniformity on the hypersphere based on a Stein characterization associated with the Laplace-Beltrami operator. We identify a sufficient class of test funct…
Tests for multivariate normality -- a critical review with emphasis on weighted -statistics
Bruno Ebner, Norbert Henze
This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of sever…
On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality
Bruno Ebner, Norbert Henze
The Shapiro--Wilk test (SW) and the Anderson--Darling test (AD) turned out to be strong procedures for testing for normality. They are joined by a class of tests for normality prop…
Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces
Philip Dörr, Bruno Ebner, Norbert Henze
We study a novel class of affine invariant and consistent tests for normality in any dimension. The tests are based on a characterization of the standard -variate normal distrib…
A unified approach to goodness-of-fit testing for spherical and hyperspherical data
Bruno Ebner, Norbert Henze, Simos Meintanis
We propose a general and relatively simple method for the construction of goodness-of-fit tests on the sphere and the hypersphere. The method is based on the characterization of pr…
Multivariate goodness-of-fit on flat and curved spaces via nearest neighbor distances
Bruno Ebner, Norbert Henze, Joseph E. Yukich
We present a unified approach to goodness-of-fit testing in and on lower-dimensional manifolds embedded in based on sums of powers of weighted volumes…
Minimum -distance estimators for non-normalized parametric models
Steffen Betsch, Bruno Ebner, Bernhard Klar
We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recent…
A Stein Characterization-type Omnibus Tests for the Discrete Pareto Distribution
Deepesh Bhati, Bruno Ebner, Sakshi Khandelwal
The discrete Pareto (or Zeta, Zipf) distribution, arises naturally in modeling rank-frequency data across diverse fields such as linguistics, demography, biology, and computer scie…
On combining the zero bias transform and the empirical characteristic function to test normality
Bruno Ebner
We propose a new powerful family of tests of univariate normality. These tests are based on an initial value problem in the space of characteristic functions originating from the f…
Stein's Method of Moments
Bruno Ebner, Adrian Fischer, Robert E. Gaunt +2
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for margin…
Logistic or not logistic?
James S. Allison, Bruno Ebner, Marius Smuts
We propose a new class of goodness-of-fit tests for the logistic distribution based on a characterisation related to the density approach in the context of Stein's method. This cha…
Testing normality in any dimension by Fourier methods in a multivariate Stein equation
Bruno Ebner, Norbert Henze, David Strieder
We study a novel class of affine invariant and consistent tests for multivariate normality. The tests are based on a characterization of the standard -variate normal distributio…
Characterizations of non-normalized discrete probability distributions and their application in statistics
Steffen Betsch, Bruno Ebner, Franz Nestmann
From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify thos…
Weibull or not Weibull?
Bruno Ebner, Adrian Fischer, Norbert Henze +1
We propose novel goodness-of-fit tests for the Weibull distribution with unknown parameters. These tests are based on an alternative characterizing representation of the Laplace tr…
A new test of multivariate normality by a double estimation in a characterizing PDE
Philip Dörr, Bruno Ebner, Norbert Henze
This paper deals with testing for nondegenerate normality of a -variate random vector based on a random sample of . The rationale of the test is that the…
A new characterization of the Gamma distribution and associated goodness of fit tests
Steffen Betsch, Bruno Ebner
We propose a class of weighted -type tests of fit to the Gamma distribution. Our novel procedure is based on a fixed point property of a new transformation connected to a Stei…
Fixed point characterizations of continuous univariate probability distributions and their applications
Steffen Betsch, Bruno Ebner
By extrapolating the explicit formula of the zero-bias distribution occurring in the context of Stein's method, we construct characterization identities for a large class of absolu…
Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution
Bruno Ebner, Lena Eid, Bernhard Klar
We introduce a new characterization of the Cauchy distribution and propose a class of goodness-of-fit tests to the Cauchy family. The limit distribution is derived in a Hilbert spa…
High-dimensional Sobolev tests on hyperspheres
Bruno Ebner, Eduardo GarcÃa-Portugués, Thomas Verdebout
The paper studies Sobolev tests for uniformity on high‑dimensional hyperspheres, deriving their asymptotic null distribution, consistency, and power against von Mises‑Fisher altern…
A general maximal projection approach to uniformity testing on the hypersphere
Jaroslav Borodavka, Bruno Ebner
We propose a novel approach to uniformity testing on the -dimensional unit hypersphere based on maximal projections. This approach gives a unifying view on t…
Eigenvalues approximation of integral covariance operators with applications to weighted statistics
Bruno Ebner, MarÃa Dolores Jiménez-Gamero, Bojana MiloÅ¡eviÄ
Finding the eigenvalues connected to the covariance operator of a centred Hilbert-space valued Gaussian process is genuinely considered a hard problem in several mathematical disci…
Is the Gompertz family a good fit to your data?
Dennis Dobler, Bruno Ebner
That data follow a Gompertz distribution is a widely used assumption in diverse fields of applied sciences, e.g., in biology or when analysing survival times. Since misspecified mo…