Minimax Euclidean separation rates for testing convex hypotheses in R-d
- We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a closed convex subset C of R-d. We adopt a minimax point of view and our primary objective is to describe the smallest Euclidean distance between the null and alternative hypotheses such that there is a test with small total error probability. In particular, we focus on the dependence of this distance on the dimension d and variance 1/n giving rise to the minimax separation rate. In this paper we discuss lower and upper bounds on this rate for different smooth and non-smooth choices for C.
| Author details: | Gilles BlanchardGND, Alexandra CarpentierORCiDGND, Maurilio Gutzeit |
|---|---|
| DOI: | https://doi.org/10.1214/18-EJS1472 |
| ISSN: | 1935-7524 |
| Title of parent work (English): | Electronic journal of statistics |
| Publisher: | Institute of Mathematical Statistics |
| Place of publishing: | Cleveland |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/11/07 |
| Publication year: | 2018 |
| Release date: | 2022/02/24 |
| Tag: | Gaussian sequence model; Minimax hypothesis testing; nonasymptotic minimax separation rate |
| Volume: | 12 |
| Issue: | 2 |
| Number of pages: | 23 |
| First page: | 3713 |
| Last Page: | 3735 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1294]; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)German Research Foundation (DFG) [314838170, GRK 2297 MathCoRe] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Gold Open-Access |
| License (German): |  CC-BY - Namensnennung 4.0 International |
