Minimax Rate for Density Estimation under Wasserstein Contamination
What is the minimax optimal error rate for density estimation when observations are perturbed by Wasserstein-bounded contaminations? Chao and Dobriban's 2023 preprint left a gap between upper and lower bounds; the sharp rate is now derived, closing the problem.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Mathematical statistics
- Posed by
- Patrick Chao, Edgar Dobriban
- Year posed
- 2023
- Years open
- 2y
- Solved
- 2025-11-24
- Model
- GPT-5 Pro
- Vendor
- OpenAI
- Collaborators
- Edgar Dobriban
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
A note written expressly to document the workflow: starting October 2025, "making significant use of GPT-5 Pro, we were able to derive the minimax optimal error rate." The model suggested calculations the authors had not thought of and techniques unfamiliar to them; the note also records the AI's limitations in its own section.