AI referee report
on “Uniform Estimation and Honest Inference in Regression Discontinuity with a Mismeasured Score”
The verified uniform frontier is a substantial theoretical contribution, while publication readiness requires sharper comparative positioning, an operational assessment of the finite-sample certificate, and a more economical presentation.
Summary
The paper characterizes matched minimax absolute estimation risk and honest connected-interval expected length for a latent-cutoff effect under known Gaussian measurement error on a precisely specified benchmark. Its observable construction and uniform comparison across sample sizes, noise scales, and regime interfaces form a coherent contribution. The principal claims faithfully preserve the verified conditions, including the benchmark domain of attainment and the lower-bound interpretation of the larger-class embedding. A major revision should establish the contribution's relationship to existing endpoint methods and make the explicit certificate's practical magnitude assessable.
Strengths
- The simultaneous comparison over every admissible sample size and noise scale gives a unified account of direct, intermediate, and compact-support precision.
- Estimation and honest expected interval length receive matching bounds on the same clearly specified law class.
- The estimator, denominator stabilization, public selection rule, and interval are explicitly defined and observable.
- The exposition consistently preserves known calibration, global regularity, binary outcomes, independent sampling, and fixed smoothness as conditions of attainment.
- The dedicated early related-work section engages several close competitors through their targets, assumptions, losses, and theorem-level conclusions.
- The application is accurately presented as a prospective eligibility-effect benchmark conditional on substantive modeling restrictions.
Findings
The contribution's relationship to existing endpoint inverse methods remains unresolved. The boundary-deconvolution paragraph describes constructions and error criteria without giving their relevant rates and conditions, while the limitations section expressly defers the systematic comparison. The supplied literature context also identifies deconvolution regression ratios and convolution-model linear-functional estimation as methodological antecedents that deserve direct engagement.
Suggested fix
Complete a focused primary-source comparison with boundary deconvolution, deconvolution regression ratios, and convolution-model linear-functional estimation. State the relevant support conditions, smoothness restrictions, endpoint losses, noise assumptions, and upper/lower bounds with exact locators. Then identify which elements of the delivered benchmark frontier and honest-length result constitute the contribution. Preserve the existing boundary on priority claims wherever source evidence remains unresolved.
The explicit certificate is a central contribution, but its operational magnitude is deferred to a separate numerical study. The large fixed coefficients, index-zero fallback, and high-order polynomial correction make the sample sizes at which selection produces informative precision important for assessing the methodological significance of this construction.
Suggested fix
Provide a reproducible deterministic evaluation of the public radius over a prespecified grid of sample sizes, noise scales, and smoothness exponents. Report the selected index, radius, fallback regions, and comparison with the resolution rate. Document numerical stability for polynomial evaluation and derivative integrals, and use the results to explain the certificate's finite-sample interpretation without extending its theorem scope.
The sentence “The upper and lower constructions therefore change regimes at the same support interface” suggests identical construction-level transition thresholds. The upper procedure uses weights on the fixed unit interval, whereas the lower witness uses the distinct support rule with its explicit factor of eight. The common resolution equation establishes a matched rate characterization; it does not identify these construction thresholds numerically.
Suggested fix
Describe support saturation as explaining the compact branch up to comparison constants, and attribute the exact interfaces to the stated noise-cost equation. For example: “Support saturation explains the compact branch, while the upper and lower envelope comparisons use the same piecewise noise cost.”
Repeated model descriptions, duplicated frontier statements, the precision handle, and extensive surrounding restatements obscure the main statistical argument. Extended-real conversion bookkeeping also occupies substantial space in the main direct-experiment statement despite its role as a specialization of the frontier.
Suggested fix
Retain one prominent frontier statement and one consolidated model definition. Move the direct-experiment specialization and consolidated verification statement to the verification appendix, replacing their main-text repetition with concise cross-references. Reduce appendix commentary that repeats complete conclusions already stated, while preserving the formal objects and their exact conditions.
The full marked likelihood statement calls g_m the cancellation polynomial “of \cref{obj:lem:classical-legendre-facts},” although that environment establishes Legendre identities and the cancellation block is defined in Lemma 5. The later corrective paragraph leaves the erroneous formal-statement pointer in place.
Suggested fix
Change the cancellation-polynomial reference to Lemma 5, retaining the Legendre reference where those identities are invoked. Remove the compensating paragraph once the statement points directly to the defining environment.
The extension and alternative-law definitions use the cancellation polynomial and amplitude before displaying their formulas. Separately, the precision handle quantifies over all natural sample sizes and polynomial indices and all real noise scales, while its reader-facing component definitions use admissible sample sizes, positive indices, and the declared noise range. This creates avoidable forward dependencies and domain ambiguity.
Suggested fix
Display the cancellation block, normalizer, amplitude, and parameter ranges before the extension and alternative laws, leaving their properties in the subsequent lemma. Restrict the precision summary to n at least two, noise in the declared interval, and positive kernel indices, or replace it with a concise index of existing definitions that preserves each object's stated domain.
The ordinary transition prose says the next theorem “does not introduce a separate frontier,” contrary to the affirmative contribution-framing contract.
Suggested fix
Replace that sentence with an affirmative description, such as: “The next result records the direct-experiment specialization of \cref{obj:thm:uniform-frontier}.”
The transition begins “he next result establishes its rate,” with a missing initial letter and an unclear antecedent for “its.”
Suggested fix
Delete this redundant transition after revising the preceding paragraph, or write “The next result establishes the direct-experiment rate and its attainment at zero noise.”
Questions for the authors
- Which components of the endpoint frontier and honest-length characterization remain distinct after aligning existing boundary and linear-functional results with the benchmark's support, nuisance-density restrictions, and loss?
- For which calibrated sample sizes and noise scales does the explicit public selection choose a positive index, and what precision does its certificate then deliver?
- Can the mathematical presentation retain a single main frontier statement while collecting the formal representation details in the verification appendix?
Review history
| Round | Date | Score | Findings |
|---|---|---|---|
| 1 | 1 Oct 2026 | 7.1 | 8 |
| 2 | 1 Oct 2026 | 7.3 | 8 |
| 3 · current | 1 Oct 2026 | 7.2 | 8 |
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 e44bbe2bdeb8.