AI referee report
on “Efficient Estimation of Binary Treatment Effects under Local Differential Privacy”
The verified results establish a substantial exact efficiency characterization, while computational reproducibility, economical exposition, and evidence supporting practical trial use require substantial development.
Summary
The paper characterizes the exact fixed-privacy local asymptotic efficiency constant for the treatment-effect contrast in an interior binary randomized-trial model. Its finite nuisance-profiled optimization, sequential lower bound, private-pilot attainment, and sharp stationary output-cardinality results form a coherent contribution. The prose generally preserves the verified conditions and accurately scopes the comparator and prospective application, but the submission needs a reproducible selection procedure and a substantially more focused presentation to earn publication.
Strengths
- The stationary optimization and sequential risk bound answer the same statistical question, with attainment connecting channel design to inference.
- Nuisance profiling produces substantive support geometry, including certified regions requiring five outputs despite the four-record input alphabet.
- Exact conditional centering and pointwise Wald validity across optimal-support changes strengthen the private-pilot construction.
- The manuscript carefully distinguishes universal lower bounds, regular attainment, pointwise coverage, and stationary cardinality conclusions.
- The early related-work section engages Steinberger and Kairouz–Oh–Viswanath concretely, and the Laplace comparison accurately identifies its release-and-estimator benchmark.
Findings
The boxed algorithm takes a measurable strong-saddle selector as an input and states, “Numerical evaluation of this input requires a separately specified solver and tie-breaking rule.” Consequently, the central channel-selection step remains an abstract interface, while the discussion describes the pilot as making parameter-dependent optimization operational. The verified selector-existence result establishes theoretical feasibility; reproducible numerical execution requires an additional computational specification.
Suggested fix
Provide a reference implementation of the finite optimization with deterministic tie handling, channel-weight recovery, and reported feasibility, profiling-stationarity, and optimality residuals. Include reproducible evaluations at the certified three-output, five-output, and balanced points, and distinguish numerical tolerances from the exact selector conditions used by the attainment theorem.
Repeated definitions, assumption explanations, theorem paraphrases, and procedural descriptions obscure the central contribution. Local alternatives and scaled errors receive several overlapping definitions; the pilot appears as a formal algorithm, a boxed algorithm, and repeated explanatory passages; the proof-exposition section largely repeats result summaries before the appended proofs. This substantially increases the effort needed to follow the statistical argument.
Suggested fix
Organize the main text around one model specification, one finite optimization, one implementable estimator, and the principal efficiency and cardinality results. Consolidate repeated explanations, move totalization and indexing conventions to a technical appendix, and replace the repetitive proof-exposition section with a concise account of the mechanisms connecting the results. Preserve every verified hypothesis and conclusion during this reorganization.
The ratios 2.69 and 7.26 are correctly identified as asymptotic planning quantities. Their usefulness for recruitment decisions nevertheless depends on the finite-sample behavior of the actual pilot-selected procedure, particularly when privacy makes pilot learning difficult or estimated parameters cross support regions.
Suggested fix
Add a reproducible simulation study reporting bias, scaled mean squared error, coverage, and interval length across sample sizes, privacy budgets, assignment probabilities, and parameters near the certified support regions. Compare the implemented private-pilot procedure with the specified custom-Laplace sample mean, and use the results to qualify prospective recruitment calculations.
The sentence “Under interior assignment and positive privacy, a measurable strong-saddle selector exists” is supported by the current verified declarations, but the reader-facing exposition gives the selector conditions without explaining their jointly measurable realization. Repeated conditional language can therefore leave readers uncertain about how the established existence result connects to the procedure.
Suggested fix
Add a concise existence argument or construction explaining joint selection of weights and profiling coordinate, measurability, and extension to all real parameter pairs. Explicitly separate established selector existence from the choice of a particular selector used in the conditional attainment statements.
The frontier channel-optimization paragraph describes Amorino and the finite-alphabet testing work broadly, whereas the closest older results receive detailed conditions and theorem locators. Given the overlap in extremal-mechanism factorization and information optimization, readers need a comparably precise account of the incremental contribution.
Suggested fix
Specify the relevant theorem or section locators and the actual objectives and conditions of these recent results. Explain which existing factorization and scalar-information conclusions supply antecedents, and identify nuisance profiling, sequential contrast-risk attainment, and the sharp support certificates as the particular contributions established here.
The projected-score expression uses t before the formal environment defining it, without a first-use plain-word gloss identifying it as the real profiling coordinate. The subsequent explanation names v(t) as a direction but still leaves the role and domain of t implicit until the definition.
Suggested fix
Introduce “the real nuisance-profiling coordinate t” before the first projected-score expression and identify v(t) as its associated unit-contrast direction. Check other symbols introduced before their defining environments against the same first-use convention.
Questions for the authors
- Which deterministic solver and tie-breaking rule will implement the strong-saddle selector, and how will computed solutions be certified against its exact conditions?
- Across the intended recruitment ranges, how closely do the implemented procedure's interval lengths and coverage follow the asymptotic planning calculations?
Review history
| Round | Date | Score | Findings |
|---|---|---|---|
| 1 | 1 Oct 2026 | 6.5 | 9 |
| 2 | 1 Oct 2026 | 7.1 | 7 |
| 3 · current | 2 Oct 2026 | 7.3 | 6 |
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 53195e13ed8f.