AI referee report
on “Minimax Estimation and Honest Inference in Randomized Experiments with Missing Outcomes”
The verified arrival-and-dimension characterization is a substantial theoretical contribution, but publication requires a clearer statistical narrative, substantial compression, and a correction to the description of the converse construction.
Summary
The paper establishes matching minimax squared-error and honest connected-interval expected-length orders for balanced Bernoulli randomized experiments with binary outcomes and surrogates, unrestricted finite baseline cells, and a known MAR arrival floor in [1/2,1]. Its distinctive contribution is the uniform dependence on the arrival deficit, supported by normalized causal priors compared on the complete observed experiment. The headline claims largely respect the verified scope, and the related-work comparisons are unusually specific. The manuscript's extensive formalization-oriented exposition nevertheless obscures the statistical argument and needs substantial editorial revision.
Strengths
- The rate characterizes sample size, baseline dimension, and arrival jointly, with universal constants through the complete-arrival endpoint.
- The normalized converse preserves every observed coordinate and the arrival-deficit factor in target separation.
- The estimation and interval criteria are explicit, including finite-sample uniform coverage and worst-law expected length.
- The dedicated early related-work section discusses competitors' actual rates and conditions and gives appropriate credit for identification and polynomial methods.
- The manuscript clearly discloses the exhibited tuning threshold, large constants, and computational questions.
Findings
The presentation-level definitions of the cellwise quantities and estimator class contain exhaustive cross-reference lists spanning almost the entire paper, including later results and mutually referencing definitions. These lists suggest circular dependencies and make elementary statistical objects unnecessarily difficult to read. Repeated empty-alphabet and decidable-equality details further interrupt the model description.
Suggested fix
Replace both exhaustive lists with their immediate prerequisites: the full-data law and cell events for the conditional quantities, and the observed sample space for the estimator class. Present the positive-d statistical experiment in a compact sequence, and move empty-alphabet and representation details to the verification appendix while preserving the formal definitions and theorem conditions.
The detailed estimator construction precedes the headline theorems, while repeated explanations and elementary range, measurability, projection, and square-root calculations dominate the appendices. The novel statistical mechanism—missing-mass weighting and normalization-compatible mixture comparison—is difficult to distinguish from routine infrastructure. Discussions of unbounded real suprema are especially distracting when the defined losses and lengths are uniformly bounded.
Suggested fix
State the two frontier theorems immediately after introducing the benchmark, followed by a concise argument overview. Then present the estimator and converse mechanisms. Consolidate repeated explanations, use the established boundedness of risks and lengths in the reader-facing proofs, and place the fully expanded proof renderings in a clearly linked supplement. Retain every substantive hypothesis and the correspondence to the verified results.
The introduction states: “When the squared arrival-weighted dimension scale is at least n^{-1}, oppositely oriented pairs of baseline labels and a fixed filler label give exactly normalized priors,” and the converse appendix repeats this description across that regime. The verified theorem guarantees existential priors throughout the regime, whereas the exhibited proof uses paired priors beyond a tolerance-dependent sample-size threshold and one-label point priors for smaller samples.
Suggested fix
Describe the converse as an all-sample existential comparison assembled from a paired-prior construction at sufficiently large sample sizes and a one-label comparison at smaller sample sizes. Preserve the separate regime condition on the dimension scale and identify the threshold's dependence on the fixed mixture tolerance.
The verification note identifies a commit, toolchain, source directory, and two bundle filenames, but supplies no reader-accessible repository or archive link. These identifiers alone leave the frozen artifact difficult to retrieve.
Suggested fix
Add an immutable public repository or archive link covering the stated commit, Lean sources, crosswalk, snippets, and instructions for reproducing the formal checks. Link the presentation bundle explicitly and preserve the distinction between mapped and presentation-level objects.
The sentence “The formal proofs ... appear in the following proof appendix, so no second derivation is repeated here” uses absent-deliverable framing outside the limitations section and refers to an internal structural target without cleveref.
Suggested fix
Replace it with affirmative navigation, for example: “The proofs in \cref{sec:deferred-proofs} combine these upper bounds and lower bounds to establish both frontiers and the complete-arrival reduction.”
Review history
| Round | Date | Score | Findings |
|---|---|---|---|
| 1 | 1 Oct 2026 | 7.2 | 6 |
| 2 | 1 Oct 2026 | 6.9 | 6 |
| 3 · current | 1 Oct 2026 | 7.0 | 5 |
Every referee draw is kept: scores are noisy, so the history is shown rather than only the last or the best pass.
Read against paper.tex sha256 48819d88ffc5.