{"id":"85591ee4-32d2-4d43-8064-c62dc735e4e7","arxiv_id":"1908.00477","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A K-sample jackknife empirical likelihood test based on categorical Gini correlation is derived, with a chi-square_{K-1} null limit that avoids permutation.","lead":"The authors build a nonparametric test for whether K different groups come from the same distribution, using jackknife empirical likelihood and a Gini-based dependence measure. The test has a standard chi-square null distribution, so no permutation is needed, and simulations show it is powerful for scale differences.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 2.1's algebra appears sound under C1; the load-bearing soft spot is finite-sample calibration of the chi-square p-values, with sizes up to 0.089 at nominal 0.05 in the paper's own t5/exponential tables.","rationale":"I read the proof of Theorem 2.1 carefully and found the main matrix algebra to be correct. In particular, the contested identity A^T W0 A = A holds, and the eigenvalue calculation yielding K-1 nonzero eigenvalues is valid: Sigma0 A has first row and column zero, and the lower-right block is I - a 1^T, with eigenvalues 0 and 1 (multiplicity K-1). Thus the claimed chi-square limit is internally consistent. C1 is also sufficient for the required U-statistic CLT, since finite variance of g_k implies finite second moments of ||X|| and hence of the kernel. Lemma 6.4's covariance formula is correct. The false Remark 2.1 does not invalidate the theorem, because the proof treats the actual product in (7); the remark should be corrected but is not load-bearing. The genuinely exposed point is finite-sample calibration: the paper's own simulations show materially inflated Type I error for t5 and exponential distributions that satisfy C1. Because the practical value of the paper is the ability to compute p-values from the chi-square table without permutation, this calibration gap at n≈50 is the most serious weakness. It does not disprove the asymptotic result, but it means the central practical claim is not yet established for the distributions and sample sizes studied. I therefore keep the reader's CONDITIONAL verdict while emphasizing that the missing piece is not the theorem's algebra but a demonstration that the chi-square approximation is usable at practical sample sizes, or a stated calibration correction.","tokens_in":16679,"tokens_out":31790,"duration_ms":316209,"concrete_test":"Reproduce the null-size rows of Table 5 and Table 6 (K=3, t5 and exponential, d=1, balanced design) with 10,000 replications at n1=n2=n3=200 and n1=n2=n3=500, using the authors' dfoptim-based solver. If the empirical sizes converge to within binomial error of 0.05 (roughly 0.045-0.055), the asymptotic theorem stands and only a finite-sample caveat is needed. If sizes remain above about 0.065, the no-permutation chi-square p-values are not reliable at these sample sizes, and the paper should provide a calibration or bootstrap correction before the method is used as advertised.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central asymptotic claim is plausible: I checked the unproved matrix identity and eigenvalue claim in the proof of Theorem 2.1. With Sigma0 = [[1, a^T],[a, D]] and A as defined, Sigma0 A equals [[0, 0],[0, I - a 1^T]], whose eigenvalues are {0, 0, 1^(K-1)}; the trace is K-1, so the chi-square degrees of freedom are internally consistent. Lemma 6.4's covariance computation also checks out, and C1 is strong enough to imply finite second moments of the distance kernel, so the U-statistic CLT is not the weak point. What is least secure is the practical claim attached to the theorem: that chi-square critical values and p-values can be used without permutation. The paper's own Tables 5 and 6 show empirical null sizes of 0.076-0.089 at nominal 0.05 for t5 and exponential data with n roughly 50 per group. These distributions satisfy C1 (finite variance), so this is not merely a violation of the stated assumption; it is a failure of the chi-square approximation to be calibrated at the sample sizes the paper itself uses. Calling this a 'slight' over-size problem understates that 0.089 is a 78% inflation of the nominal level. Since the advertised advantage over permutation tests is precisely the chi-square null limit, this calibration gap is load-bearing for the method as presented.","agreement_with_reader":"partial"},"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-14T15:54:06.904825+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}