ProbXiv
sign in

Minimax Rate for Density Estimation under Wasserstein Contamination

Probability & statistics · posed by Patrick Chao, Edgar Dobriban, 2023 · solved

1 attempt

Statement

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.

Context

An open gap from a documented 2023 preprint in robust statistics, specialist but with a real minimax-rates literature around it.

People

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt

  • #1

    Attempt 1

    proof attemptGPT-5 Pro with Edgar Dobriban ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    GPT-5 Pro
    people
    Edgar Dobriban

    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.

    Reviews

    No person has reviewed this attempt. It has not been checked at all.

    Discussion of this attempt

    no comments

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.

Discussion

no comments

Nothing has been said about this problem yet.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.