Name
Abstract | ||
|---|---|---|
We address the problem of finite-sample null hypothesis significance testing on the mean element of a random variable that takes value in a generic separable Hilbert space. For this purpose, we propose a (re)definition of Hotelling’s T2 that naturally expands to any separable Hilbert space that we further embed within a permutation inferential approach. In detail, we present a unified framework for making inference on the mean element of Hilbert populations based on Hotelling’s T2 statistic, using a permutation-based testing procedure of which we prove finite-sample exactness and consistency; we showcase the explicit form of Hotelling’s T2 statistic in the case of some famous spaces used in functional data analysis (i.e., Sobolev and Bayes spaces); we demonstrate, by means of simulations, that Hotelling’s T2 exhibits the best performances in terms of statistical power for detecting mean differences between Gaussian populations, compared to other state-of-the-art statistics, in most simulated scenarios; we propose a case study that demonstrate the importance of the space into which one decides to embed the data; we provide an implementation of the proposed tools in the R package fdahotelling available at https://github.com/astamm/fdahotelling. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.jmva.2018.05.007 | Journal of Multivariate Analysis |
Keywords | Field | DocType |
62G10,62H15 | Hilbert space,Discrete mathematics,Random variable,Statistic,Permutation,Sobolev space,Separable space,Statistics,Resampling,Statistical hypothesis testing,Mathematics | Journal |
Volume | ISSN | Citations |
167 | 0047-259X | 0 |
PageRank | References | Authors |
0.34 | 22 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Alessia Pini | 1 | 6 | 2.55 |
| Aymeric Stamm | 2 | 11 | 3.76 |
| Simone Vantini | 3 | 60 | 9.26 |