The unique copula of a continuous random pair <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(X,Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> is said to be radially symmetric if and only if it is also the copula of the pair <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$(-X,-Y)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mi>X</mi> <mo>,</mo> <mo>-</mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation>. This paper revisits the recently considered issue of testing for radial symmetry. Three rank-based...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

This paper proposes a new rank-based test of extreme-value dependence. The procedure is based on the first three moments of the bivariate probability integral transform of the underlying copula. It is seen that the test statistic is asymptotically normal and its finite- and large-sample variance...

Dieses Arbeitsbuch dient dem Aufbau und der Auffrischung mathematischer Grundlagen zum Studienbeginn. Es bietet eine systematische, statistikorientierte Aufbereitung der mathematischen Grundlagen sowie eine Fülle von Anwendungsbeispielen und Aufgaben aus dem Umfeld der angewandten Statistik....

Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample...

The precision of stereological estimators based on systematic sampling is of great practical importance. This paper presents methods of data-based variance estimation for generalized Cavalieri estimators where errors in sampling positions may occur. Variance estimators are derived under...

Assessing the precision of volume estimates from systematic samples is a question of great practical importance, but statistically a challenging task due to the strong spatial dependence of the data and typically small sample sizes. The approach taken in this paper is more ambitious than earlier...