# Literature audit D — priority / novelty-threat sweep (2013 → 2026-10-28)

Method (verification task, 2026-10-28 18:47–19:05): 40+ web searches (arXiv, JMLR, AoS, JASA, Biometrika, Statistica Sinica, JCGS, QE, ReStud, TEST, CSDA; Crossref for metadata); full texts read for the 14 most relevant papers. Local dumps /tmp/litsearch/.

# Threat per candidate claim (auditor's assessment)

• C1 r-th order split-sample extrapolation of local MLEs, then average: PARTIAL→STRONG. "Debias each local estimator then average" exists: ZDW13 SAVGM (subsampling); Gu & Chen (2023) JMLR 24(387) (analytic Rilstone-type local bias correction with sample splitting, weighted by n_k Ĥ_k^{-1}; χ² limit if K = o(n²) ⇔ K = o(N^{2/3}); beats the SAVGM constant); Wu, Zhu & Wang (2023) Statistica Sinica 33:2041–2064 (delete-one jackknife within each subsample, then average; bias O(n^{-2}) + O(N^{-1}); normality under N = o(n⁴)); Li et al. (2024) review says JDS "is readily applicable to distributed computing"; Yin (2022) (analytic). The nested-subsample Vandermonde construction is Dhaene & Jochmans (2015) / Schucany–Gray–Owen (1971) / Quenouille (1956). Not found: a general r-th order split-sample extrapolation of local MLEs in divide-and-conquer with r ≥ 3 and the influence-function-preservation argument. Caveat: Hahn–Hughes–Kuersteiner–Newey (QE 2024) split-sample jackknife has twice the higher-order variance of delete-one.
• C2 debiased average + q exact-Hessian Newton steps, frontier K = o(N^{1−1/(2^{q+1} r)}): PARTIAL. Average + 1 exact step: Huang & Huo (2019) (stated k = O(√N); MSE term k⁴N^{-4} ⇒ implicitly 3/4); Zhu, Li & Wang (2021) JCGS 30(4):1004–1018, DOI 10.1080/10618600.2021.1923517 Theorem 2: TWLSE (average → one local Newton step per machine → local-Hessian-weighted average) efficient iff n/N^{1/4} → ∞, "allows K = O(N^{3/4})"; Prop. 2 iterated version with m/log N → ∞ rounds allows n = O(1); CEASE rounds frontier n^{t+2} ≫ N polylog ⇒ K = o(N^{(t+1)/(t+2)}); JLY contraction n^{-1/2}; Yin (2022) arXiv 2207.06253 Theorem 3.2: bias-adjusted one-step estimator (analytic removal of quadratic terms, pilot = average) efficient iff m = o(n²) ⇔ K = o(N^{2/3}). Nobody combines an extrapolated initial estimator with exact-Hessian Newton rounds; no joint (order, rounds) frontier; no 7/8 or 11/12 anywhere.
• C3 sharpness: PARTIAL. Necessity results exist only for plain averaging: Volgushev–Chao–Cheng (2019) Thm 3.2 + Cor 3.3; Shang–Cheng (2017); ZDW Example 1. Huang–Huo claim necessity of k = O(√N) from simulation only. Yin's 2022 Temple PhD thesis may derive a non-normal limit for one-step estimators with many centres — NOT VERIFIED (repository 403). No sharpness result for a debiased/Newton construction.
• C4 inexact Newton: PARTIAL. Single-machine Hessian: JLY Cor 3.4, Wang–Kolar–Srebro–Zhang 2017; local Hessians at local points: Zhu–Li–Wang (K = O(N^{3/4})); gradient-built Fisher information with O_p(n^{-1} + m^{-1}) error: Yin 2022; CEASE contraction p/n; Lin–Xi AEE. Quantized/compressed Hessian with a statistical K-exponent and byte count: nothing found (Alimisis–Davies–Alistarh ICML 2021 is optimization-only).
• C5 unequal sizes / misspecification: STRONG (sizes) / PARTIAL (misspecification). Weighted aggregation with unequal n_k is routine (Zhu–Li–Wang; Gu–Chen with quasi-likelihood ⇒ sandwich; Wang et al. CSDA 2021; Zhou et al. 2020; Lin–Xi; Chen–Xie 2014; Shi–Lu–Song 2018; Chen–Jing–Liu–Zhang AoS 2024 Thm 4.1). Misspecification: JLY Cor 3.4 is the sandwich; Gu–Chen quasi-likelihood; Volgushev p. 10. → present as an extension, not a contribution.
• C6 cost model (extra extrapolation level vs extra synchronization round): PARTIAL-low. Only qualitative trade-off statements (JLY p. 15; Zhu–Li–Wang p. 12; CEASE §4.3; Kal–Szabó–Guhaniyogi–Pillai–Pati 2025 bit accounting; Duchi et al. 2014, Szabó–van Zanten 2020, Cai–Wei 2024 lower bounds). No explicit decision rule found.

# Additional verified records (beyond audits A–C)

• Zhu, Xuening; Li, Feng; Wang, Hansheng (2021) "Least-Square Approximation for a Distributed System", JCGS 30(4):1004–1018, DOI 10.1080/10618600.2021.1923517 (arXiv 1908.04904v4 read): WLSE weights α_k Σ̂_k^{-1}; c₁ ≤ n_k/n ≤ c₂; Prop. 1 bias O_p(K/√N); Thm 1 efficient if n/N^{1/2} → ∞; Thm 2 TWLSE bias O_p(n^{-2}√N), efficient if n/N^{1/4} → ∞; Prop. 2 m-WLSE.
• Gu, Jia; Chen, Songxi (2023) "Distributed statistical inference under heterogeneity", JMLR 24(387):1–56 (arXiv 2209.06482v1 read): WD weights n_k Ĥ_k^{-1}; Thms 2–3 K = o(N^{1/2}); §5 analytic leading bias n_k^{-1}B_k with sample splitting; Thms 4–6 dWD/dSaC MSE ≤ C₁/(nK) + C₂/(n²K) + C₃/n³, χ² limit if K = o(n²); Cor. 1 constant beats SAVGM's (2+3r)/(2(1−r)²); likelihood and quasi-likelihood (sandwich); one round; SM §1.10 vs Huang–Huo.
• Wu, Shuyuan; Zhu, Xuening; Wang, Hansheng (2023) Statistica Sinica 33:2041–2064, DOI 10.5705/ss.202021.0257 (arXiv 2304.06231v1 read): JDS = delete-one jackknife bias estimate per subsample then average (§2.3); Thm 2 bias O(n^{-2}) + O(N^{-1}); Thm 4 normal under N = o(n⁴). Smooth functions of means.
• Yin, Z. (2022) "Communication-efficient distributed Newton-like optimization with gradients and M-estimators", arXiv 2207.06253 (read): Fisher information from gradients + M-estimators with error O_p(n^{-1} + m^{-1}); Thm 3.2 bias-adjusted one-step error O_p(n^{-3/2} + m^{-1}n^{-1/2}); efficient iff m = o(n²).
• Gao, Yuan; Liu, Weidong; Wang, Hansheng; Wang, Xiaozhou; Yan, Yibo; Zhang, Riquan (2022) "A review of distributed statistical inference", Statistical Theory and Related Fields 6(2):89–99, DOI 10.1080/24754269.2021.1974158 (read): averaging MSE C₁/N + C₂/n²; one-step C₁/N + O(n^{-4} + N^{-2}); "K = o(√N) necessary (Volgushev)"; open problem: unbalanced sizes (p. 20). Confirms no (order, rounds) frontier as of 2022.
• Li et al. (2024) "A selective review on statistical methods for massive data computation", arXiv 2403.11163 (journal NOT VERIFIED).
• Chen, Xi; Jing, Wenbo; Liu, Weidong; Zhang, Yichen (2024) AoS 52(3):922–947, DOI 10.1214/24-AOS2376 (arXiv 2210.08393v4 read): Thm 3.1 one-shot L condition; Thms 3.3–3.4 multi-round; Thm 4.1 weighted average with unequal m_ℓ.
• Wang, Zhu, Huang, Qi, Wang (2021) CSDA 162:107265, DOI 10.1016/j.csda.2021.107265 (abstract): OSUP pilot + one step; non-random unequal partitions.
• Zhou, Yu, Ma, Tian, Fan (2020) arXiv 2001.06194v2 (read): AEE K = o(√n/p_n); weighted average + Fisher scoring K = O(√(n/p_n)).
• Duan, Ning, Chen (2022) Biometrika 109(1):67–83, DOI 10.1093/biomet/asab007 (abstract): heterogeneity-aware surrogate.
• Chen, Liu, Zhang (2019) AoS 47(6):3244–3273, DOI 10.1214/18-AOS1777 (abstract): naive DC needs n = o(m²); multi-round removes.
• Chen & Xie (2014) Statistica Sinica 24:1655–1684, DOI 10.5705/ss.2013.088 (abstract). Lee, Liu, Sun & Taylor (2017) JMLR 18(5):1–30 (abstract). Dobriban & Sheng (2021) AoS 49(2):918–943, DOI 10.1214/20-AOS1984. Szabó & van Zanten (2020) AoS 48(4):2347–2380, DOI 10.1214/19-AOS1890. Cai & Wei (2022) AoS 50(4):1992–2020, DOI 10.1214/21-AOS2167. Duchi, Jordan, Wainwright & Zhang (2014) arXiv 1405.0782. Kal, Szabó, Guhaniyogi, Pillai & Pati (2025) arXiv 2508.17073. Banerjee, Durot & Sen (2019) AoS 47(2):720–757, DOI 10.1214/17-AOS1633. Minsker (2019) EJS 13:5213–5252, DOI 10.1214/19-EJS1647. Luo & Song (2020) JRSS-B 82(1):69–97, DOI 10.1111/rssb.12352. Tan, Battey & Zhou (2022) JMLR 23(272):1–61. Alimisis, Davies & Alistarh (2021) ICML, arXiv 2102.07214. Lin & Li (2023) TEST 32(2):726–758, DOI 10.1007/s11749-023-00850-5. Tu, Liu, Mao & Chen (2021) JMLR 22(84):1–67.

Searches with no relevant hit: "Richardson extrapolation" + distributed; "split-sample jackknife" + distributed; "K = o(N^{7/8})"; distributed pseudo-MLE/sandwich as a topic; quantized-Hessian one-step with asymptotic normality.