Abstract
We study estimation methods under communication constraints in a distributed version of the nonparametric random design regression model. We derive minimax lower bounds and exhibit methods that attain those bounds. Moreover, we show that adaptive estimation is possible in this setting.
Original language | English |
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Pages (from-to) | 2347-2380 |
Number of pages | 34 |
Journal | Annals of Statistics |
Volume | 48 |
Issue number | 4 |
Early online date | 14 Aug 2020 |
DOIs | |
Publication status | Published - Aug 2020 |
Funding
Acknowledgements. We would like to thank the Associate Editor and the referees for their careful review of the various versions of this paper and for their valuable comments and suggestions. Both authors were supported by the Netherlands Organization of Scientific Research NWO. The research leading to these results has received funding from the European Research Council under ERC Grant Agreement 320637.
Funders | Funder number |
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Netherlands Organization of Scientific Research NWO | |
Seventh Framework Programme | 320637 |
European Research Council |
Keywords
- Adaptation
- Communication constraints
- Distributed computation
- Minimax rates
- Nonparametric regression