TY  - JOUR
A1  - Gaigall, Daniel
T1  - Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data
JF  - Metrika
N2  - We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
KW  - Marginal homogeneity test
KW  - Crámer–von-Mises distance
KW  - Paired sample
KW  - Incomplete data
KW  - Resampling test
Y1  - 2019
U6  - http://dx.doi.org/10.1007/s00184-019-00742-5
SN  - 1435-926X
VL  - 2020
IS  - 83
SP  - 437
EP  - 465
PB  - Springer
ER  - 
TY  - THES
A1  - Gaigall, Daniel
T1  - On selected problems in multivariate analysis
N2  - Selected problems in the field of multivariate statistical analysis are treated. Thereby, one focus is on the paired sample case. Among other things, statistical testing problems of marginal homogeneity are under consideration. In detail, properties of Hotelling‘s T² test in a special parametric situation are obtained. Moreover, the nonparametric problem of marginal homogeneity is discussed on the basis of possibly incomplete data. In the bivariate data case, properties of the Hoeffding-Blum-Kiefer-Rosenblatt independence test statistic on the basis of partly not identically distributed data are investigated. Similar testing problems are treated within the scope of the application of a result for the empirical process of the concomitants for partly categorial data. Furthermore, testing changes in the modeled solvency capital requirement of an insurance company by means of a paired sample from an internal risk model is discussed. Beyond the paired sample case, a new asymptotic relative efficiency concept based on the expected volumes of multidimensional confidence regions is introduced. Besides, a new approach for the treatment of the multi-sample goodness-of-fit problem is presented. Finally, a consistent test for the treatment of the goodness-of-fit problem is developed for the background of huge or infinite dimensional data.
KW  - Paired sample
KW  - Marginal homogeneity
KW  - Incomplete data
KW  - Asymptotic relative efficiency
KW  - Volumes of confidence regions
Y1  - 2023
U6  - http://dx.doi.org/10.15488/14304
N1  - Gottfried Wilhelm Leibniz Universität Hannover
ER  -