papers

Publications (33)

stat.ME2017

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…

stat.ME2024

A new flexible class of kernel-based tests of independence

Marija Cuparić, Bruno Ebner, Bojana Milošević

Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. I…

stat.ME2021

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…

stat.ME2020

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…

math.ST2025

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…

stat.ME2023

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…

stat.ME2018

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…

math.ST2021

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…

math.ST2023

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…

math.ST2020

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…

stat.ME2022

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…

math.ST2026

On Stein's test of uniformity on the hypersphere

Paul Axmann, Bruno Ebner, Eduardo García-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…

math.ST2020

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…

math.ST2021

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…

stat.ME2019

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…

math.ST2023

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…

stat.ME2016

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…

math.ST2020

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…

stat.ME2026

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…

math.ST2020

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…

math.ST2024

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…

math.ST2021

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…

math.ST2020

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…

stat.ME2021

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…

math.ST2022

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…

math.ST2019

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…

stat.ME2018

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…

math.ST2019

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…

math.ST2021

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…

math.ST2026

High-dimensional Sobolev tests on hyperspheres

Bruno Ebner, Eduardo García-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…

#high-dimensional statistics#spherical data#sobolev tests#uniformity testing
math.ST2023

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…

math.ST2024

Eigenvalues approximation of integral covariance operators with applications to weighted statistics

Bruno Ebner, María Dolores Jiménez-Gamero, Bojana Milošević

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…

math.ST2023

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…