{"id":"66c37e90-e7ee-4b7b-bdac-7875a883c00d","arxiv_id":"2601.14013","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A quantile-winsorized max-test controls asymptotic size under contamination with m>2 moments, matches the power of the standard max-test under stronger conditions, and allows dimension to grow exponentially with sample size.","lead":"The paper proposes a max-test using quantile-winsorized observations for testing whether the mean of a high-dimensional random vector is zero, which controls asymptotic size under adversarial contamination and heavy tails while requiring only m>2 moments. It shows this robust test achieves identical asymptotic power to the standard max-test under the stronger conditions where the latter is valid, and examines bootstrap critical values.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Quantile-winsorizing at non-vanishing levels may shift the centering of the max-statistic, breaking exact asymptotic power equivalence even under no contamination.","rationale":"The reader's weakest assumption correctly flags the contamination bound, but the 'robustness for free' claim is most sensitive to the no-contamination equivalence step rather than the adversarial case. The proposed check directly tests whether the two power characterizations coincide under the intersection of assumptions.","tokens_in":1628,"tokens_out":368,"duration_ms":32077,"concrete_test":"Extract the explicit form of the asymptotic power function for both tests (presumably in the main theorems or §4–5). Under a simple Gaussian design with no contamination, numerically evaluate both power curves at the same local alternatives; if they differ by more than 0.05 in total variation for any sequence of alternatives where the standard test has power in (0.2,0.8), the equivalence fails.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that, under the stronger conditions validating the standard max-test (higher moments, no contamination), the quantile-winsorized version yields an identical limiting power function. If the winsorizing quantiles are fixed (e.g., fixed alpha > 0), each coordinate mean is altered by a positive amount equal to the tail integral beyond the quantile; this bias remains after normalization and, when taking the coordinate-wise maximum over p = exp(o(n)) dimensions, perturbs the extreme-value limit used for both size and power. The paper must therefore either let the winsorizing proportion vanish with n or prove that the bias term is negligible uniformly in the high-dimensional regime; neither is visible from the abstract and would be the least secure step in the equivalence argument.","agreement_with_reader":"partial"},"referee_report":{"model":"grok-4.3","summary":"The manuscript studies testing the mean of a high-dimensional vector equal to zero under adversarial contamination and heavy tails. It proposes a max-test based on quantile-winsorized observations that controls asymptotic size with only m>2 moments while allowing dimension p to grow exponentially in sample size n. The paper fully characterizes the asymptotic power function of the proposed test and, as a benchmark, derives the corresponding characterization for the standard (non-robust) max-test. It concludes that robustness is obtained for free: under the stronger conditions validating the standard max-test, the quantile-winsorized version has identical asymptotic power. Bootstrap critical values are also analyzed, with the result that they never decrease power and can strictly improve it in highly correlated designs.","tokens_in":1805,"tokens_out":518,"duration_ms":20881,"significance":"If the derivations hold, the result is significant for high-dimensional inference. It supplies explicit power characterizations that permit direct comparison between robust and non-robust procedures, shows that exponential dimension growth is compatible with size control under contamination, and demonstrates that a simple winsorization step can restore robustness without first-order power loss. The bootstrap analysis adds practical insight. These features address a genuine gap between theoretical robustness guarantees and the power requirements of high-dimensional testing.","major_comments":[{"comment":"§3 (asymptotic power characterization): the claim that the robust test has identical limiting power to the standard max-test under the stronger (no-contamination, higher-moment) regime requires that any centering shift induced by quantile winsorization at fixed levels α>0 is asymptotically negligible uniformly over p=exp(o(n)) coordinates. The tail-integral bias per coordinate remains after normalization and can perturb the extreme-value limit of the maximum; the manuscript must either let the winsorizing proportion vanish with n or supply the uniform negligibility argument that keeps the limiting power function unchanged.","section":"§3"}],"minor_comments":[{"comment":"The precise definition of the winsorized observations (including how the quantiles are estimated) and the exact normalization constants used for the max-statistic should be stated explicitly before the main theorems.","section":"§2"},{"comment":"Figure 1 (or the corresponding simulation panel) would benefit from an additional curve showing the standard max-test under contamination to visually confirm the size distortion that the robust version corrects.","section":"Simulation section"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comment below and believe the point can be resolved by elaborating the existing argument.","responses":[{"response":"We appreciate the referee's observation on the potential centering bias. Under the stronger regime (no contamination and m>4 moments) that validates the standard max-test, the fixed-α quantile-winsorization bias per coordinate is of smaller order than (log p)^{-1/2} uniformly in p=exp(o(n)). This follows from the higher-moment integrability controlling the tail integrals beyond the fixed quantiles; after centering and scaling, the bias term vanishes in the extreme-value limit and does not alter the Gumbel distribution or the power function. We will add an explicit lemma establishing this uniform negligibility in the revised §3 to make the argument fully transparent.","revision_made":"yes","referee_comment":"[§3] §3 (asymptotic power characterization): the claim that the robust test has identical limiting power to the standard max-test under the stronger (no-contamination, higher-moment) regime requires that any centering shift induced by quantile winsorization at fixed levels α>0 is asymptotically negligible uniformly over p=exp(o(n)) coordinates. The tail-integral bias per coordinate remains after normalization and can perturb the extreme-value limit of the maximum; the manuscript must either let the winsorizing proportion vanish with n or supply the uniform negligibility argument that keeps the limiting power function unchanged."}],"tokens_in":1349,"tokens_out":331,"duration_ms":26605,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that the authors show a max-test based on quantile-winsorized observations controls asymptotic size under adversarial contamination with only m>2 moments and dimension growing exponentially in n, while delivering the same limiting power as the usual sample-average max-test under the stronger conditions where the latter is valid. They also give explicit power functions for both versions and examine bootstrap critical values, which never reduce power and can improve it in highly correlated cases. This equivalence result and the full power characterization look like the genuinely new pieces relative to earlier max-test work. The derivations appear to rest on standard extreme-value arguments applied after the winsorizing step, and the bootstrap findings are a useful practical addition. The soft spot is the handling of the winsorizing bias. If the quantiles stay at fixed positive levels, each coordinate mean picks up a nonzero tail integral that could shift the centering of the max statistic when p is exponentially large; the paper needs to show either that the proportion vanishes with n or that the bias term is negligible uniformly in the high-dimensional limit. The abstract does not make this step explicit, so the exact equivalence claim rests on details that are not visible here. If those details check out in the proofs, the central argument holds; if not, the power equivalence is only approximate. This paper is aimed at researchers working on high-dimensional testing and robust inference in statistics and econometrics. It has enough new technical content and careful asymptotics to deserve a serious referee rather than a desk reject, even if the bias control needs tightening in revision.","headline":"The quantile-winsorized max-test matches the standard version's asymptotic power while adding robustness to contamination and heavy tails.","tokens_in":2253,"tokens_out":381,"would_cite":false,"duration_ms":18445,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"Theorem 4.1: asymptotic size and identical power function characterization for φ_{n,W} under log(d)/n^{(m-2)/(5m-2)}→0 and √(n log d) η_n^{1-1/m}→0"},{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/ArithmeticFromLogic.lean","rs_theorem":"embed_strictMono_of_one_lt","paper_passage":"Gaussian approximation (8) and (16) equating power of arithmetic-mean and winsorized max-tests to P(‖Σ_0^{1/2}Z + √n D^{-1}μ‖_∞ > c_{n,1-α})"}],"headline":"High-dimensional robust max-testing via quantile-winsorizing; no structural overlap with RS forcing chain","alignment":"orthogonal","rationale":"The paper's core machinery (normalized winsorized means S_{n,W}, Gaussian approximations over hyperrectangles for power functions, bootstrap critical values c^B_{n,1-α}, and the 'robustness for free' equivalence under m>4 moments and d=o(n^{m/2-1})) operates entirely within classical extreme-value and Berry-Esseen theory for self-normalized sums. It never invokes recognition cost J(x)=½(x+x^{-1})−1, φ-ladder identities, 8-tick periodicity, or any parameter-free derivation of constants. The domain (adversarial contamination, heavy-tail max-tests, exponential dimension growth) lies outside the RS forcing theorems (reality_from_one_distinction, AbsoluteFloorClosure, AlexanderDuality, Cost.FunctionalEquation). No contradiction arises; the constructions are simply disjoint.","tokens_in":70755,"confidence":"high","tokens_out":436,"duration_ms":19477,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A quantile-winsorized max-test achieves robustness to adversarial contamination in high dimensions without sacrificing asymptotic power.","keywords":["high-dimensional mean testing","adversarial contamination","quantile winsorizing","max-test","asymptotic power","heavy tails","bootstrap critical values","robustness"],"falsifier":"A high-dimensional Monte Carlo study with m=2.5 moments and fixed adversarial contamination in which the robust test's empirical rejection rate under the alternative falls measurably below the standard max-test's rate while both control size.","tokens_in":2534,"feed_emoji":"","tokens_out":623,"duration_ms":22409,"temperature":0.7,"pith_summary":"Standard max-tests based on sample averages lose size control when observations suffer heavy tails or adversarial contamination. The paper replaces averages with quantile-winsorized versions inside the max statistic. This version controls asymptotic size with only m>2 moments and lets dimension grow exponentially in sample size. Its asymptotic power equals that of the ordinary max-test precisely when the ordinary test is valid. Bootstrap critical values never reduce power and can raise it in strongly correlated settings.","feed_headline":"Quantile-winsorized max-test matches standard power","feed_subtitle":"Robust version controls size under contamination and heavy tails while delivering identical asymptotic power when the ordinary test applies.","key_machinery":"The quantile-winsorized max-test statistic, formed by replacing each coordinate average with a winsorized version at fixed quantiles before taking the coordinate-wise maximum.","core_discovery":"The max-test based on quantile-winsorized observations controls asymptotic size under adversarial contamination and heavy tails while requiring only m>2 moments and allowing the dimension to grow exponentially with sample size. Its asymptotic power function coincides with that of the standard max-test under the stricter conditions that validate the standard test, so that robustness is obtained at no first-order asymptotic power cost.","pith_inferences":["The same winsorizing device could be inserted into other coordinate-wise high-dimensional statistics without changing their limiting power under clean data.","In practice, analysts facing possible contamination can default to the robust version with no detectable power penalty on uncontaminated data.","The result suggests that careful truncation can neutralize worst-case contamination while preserving the exact local power envelope of the untruncated procedure."],"forward_implications":["The robust test maintains asymptotic size control under arbitrary adversarial contamination that respects the winsorizing bounds.","Asymptotic power equals the standard max-test's power exactly when the standard test is valid.","Bootstrap critical values never lower first-order asymptotic power and strictly raise it in designs with extreme coordinate correlations.","Dimension may grow exponentially with sample size while size and power characterizations remain valid."],"fun_headline_variants":["Winsorized max-test matches standard asymptotic power","Robust max-test via quantile winsorization controls size and power","Quantile-winsorized max-test delivers identical power under robustness","Max-tests on winsorized data robust to contamination with full power","High-dimensional robust max-test retains standard test power"],"cache_read_input_tokens":64,"weakest_assumption_plain":"The data have at least three moments and any adversarial contamination stays inside the quantile bounds used for winsorizing.","fun_headline_variants_meta":{"raw":{"variants":["Winsorized max-test matches standard asymptotic power","Robust max-test via quantile winsorization controls size and power","Quantile-winsorized max-test delivers identical power under robustness","Max-tests on winsorized data robust to contamination with full power","High-dimensional robust max-test retains standard test power"]},"model":"grok-4.3","cost_usd":0.004741,"raw_usage":{"total_tokens":2301,"prompt_tokens":594,"num_sources_used":0,"completion_tokens":80,"cost_in_usd_ticks":47412000,"prompt_tokens_details":{"text_tokens":594,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1627,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":594,"tokens_out":80,"duration_ms":10601,"temperature":1.0,"reasoning_tokens":1627,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-16T12:45:50.640885+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A high-dimensional Monte Carlo study with m=2.5 moments and fixed adversarial contamination in which the robust test's empirical rejection rate under the alternative falls measurably below the standard max-test's rate while both control size.","supporting_citations":[],"review_version":1}