- Thesis:
- Bachelor in Mathematics
- Author:
- Moritz Haas
- Title:
- Fréchet Analysis of Variance for random objects
- Supervisors:
- Christof Schötz and Jan JOHANNES
- Abstract:
- Fréchet mean and variance can be seen as a generalization of mean
and variance for metric spaces devoid of algebraic structures. Mainly
following Dubey and Müller (2017) we derive a central limit theorem under mild
regularity conditions using empirical process theory. This result
leads to a p-sample test for metric space valued data objects for
equality of distributions, which is intended to be suitable for
comparing means and variances simultaneously.
Further emphasis is laid on the structure of the proposed test and its connection to one-way ANOVA and Levene’s test in the Euclidean case. Finally, we visualise and verify our analysis of the strengths and weaknesses of the proposed test in simulation studies with Euclidean data. - References:
- Dubey and Müller. Fréchet analysis of variance for random objects. Technical report, arXiv:1710.02761, 2017.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |