1% ============================================================================2% UQO Working Paper No. 28 — Beyond One-Step Distributed Maximum Likelihood3% Preamble = UQO template (Recherche-UQO/HARMONISATION.md) + amsthm environments + algorithmic4% 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--- notation macros66\newcommand{\E}{\mathbb{E}}67\newcommand{\Var}{\operatorname{Var}}68\newcommand{\Cov}{\operatorname{Cov}}69\newcommand{\R}{\mathbb{R}}70\newcommand{\N}{N}71\newcommand{\dd}{\mathrm{d}}72\newcommand{\norm}[1]{\lVert #1 \rVert}73\newcommand{\abs}[1]{\lvert #1 \rvert}74\newcommand{\thetahat}{\widehat{\theta}}75\newcommand{\thetaN}{\widehat{\theta}_N}76\newcommand{\pilot}[1]{\theta^{(0)}_{#1}}77\newcommand{\iter}[2]{\theta^{(#2)}_{#1}}78\newcommand{\op}{O_p}79\newcommand{\smallop}{o_p}80\newcommand{\pto}{\xrightarrow{\;p\;}}81\newcommand{\dto}{\Rightarrow}82\newcommand{\alphafr}[2]{\alpha(#1,#2)}83\DeclareMathOperator*{\argmax}{arg\,max}84\DeclareMathOperator{\tr}{tr}85\DeclareMathOperator{\diag}{diag}86\newcommand{\Jr}[1]{J_{#1}}87\newcommand{\Amp}{A_r}88\newcommand{\betar}{\beta_r}8990% ============================================================================91% METADATA92% ============================================================================93\newcommand{\WPnumber}{28}94\newcommand{\WPtitle}{Beyond One-Step Distributed Maximum Likelihood: Local Bias Cancellation, Global Synchronization, and the Price of Inexact Curvature}95\newcommand{\WPsubtitle}{A joint order--round frontier, its sharpness in an exact model, and measured communication costs}96\newcommand{\WPdate}{October 2026}97\newcommand{\WPversion}{1.0}98\newcommand{\WPabstract}{%99 \input{sections/abstract}%100}101\newcommand{\WPkeywords}{distributed estimation, maximum likelihood, split-sample jackknife, one-step Newton estimator, communication complexity, asymptotic equivalence, Monte Carlo}102\newcommand{\WPjel}{C13, C15, C55, C63}103\newcommand{\WPauthor}{Simon-Pierre Boucher}104\newcommand{\WPaffiliation}{%105 Département des sciences administratives\\106 Université du Québec en Outaouais%107}108\newcommand{\WPemail}{simon-pierre.boucher@uqo.ca}109\newcommand{\WPaddress}{%110 Gatineau -- Pavillon Alexandre-Taché\\111 283, boulevard Alexandre-Taché\\112 Gatineau, Québec, Canada J9A 1L8%113}114\hypersetup{pdftitle={Beyond One-Step Distributed Maximum Likelihood: Local Bias Cancellation, Global Synchronization, and the Price of Inexact Curvature}, pdfauthor={Simon-Pierre Boucher}}115116\input{tables/numbers}117118\begin{document}119\input{sections/titlepage}120\input{sections/provenance}121\input{sections/introduction}122\input{sections/literature}123\input{sections/environment}124\input{sections/construction}125\input{sections/results}126\input{sections/exactmodel}127\input{sections/inexact}128\input{sections/costmodel}129\input{sections/montecarlo}130\input{sections/benchmarks}131\input{sections/robustness}132\input{sections/discussion}133\input{sections/conclusion}134135\newpage136\bibliography{references}137138\begin{appendices}139\input{appendices/proofs}140\input{appendices/exponential}141\input{appendices/algorithms}142\input{appendices/replication}143\end{appendices}144\end{document}145