papers: honesty + citation follow-up (paper-1 supersession, reverse-import, 2022 priority)

docs/papers/schur-likelihood/index.html

@@ -64,6 +64,25 @@ <h1>Schur Covariance Evaluation</h1><div class="subtitle">A
 several-fold lower out-of-sample portfolio variance once the dimension
 rivals the sample size.</p></div>
 
+<blockquote>
+<p><em>Note (added 2026, retained as a historical record).</em> The
+held-out-likelihood-versus-Schur <em>selection</em> contrast of
+Sections 4–5 does not survive scrutiny. In controlled follow-up
+experiments the full likelihood’s poor showing there is an artifact of
+judging by portfolio <em>variance</em> rather than by likelihood
+(objective mismatch), not a failure of the likelihood as a criterion:
+restricted to well-conditioned candidates and judged on its own terms it
+is in fact the better selector, and—contrary to a suspicion we briefly
+held—it does not select ill-conditioned estimates (the held-out
+likelihood penalises them). Two further corrections: the
+Schur–Ledoit–Wolf estimator of Section 6, as implemented, is cross-block
+<em>entry</em> shrinkage (a Schäfer–Strimmer-style operation), not the
+structured Schur damping it is named for; and that structured damping is
+viable only with a regularised hedge. The durable contributions are the
+closed-form reliability <span class="math inline">\gamma^\star</span>
+(Section 3) and the estimator family. See the companion note <em>Two
+Sides of Schur Damping</em> for the corrected and unified account.</p>
+</blockquote>
 <h2 id="the-high-dimensional-failure-of-the-gaussian-likelihood">The
 high-dimensional failure of the Gaussian likelihood</h2>
 <p>A correlation matrix is the hard part of a covariance matrix:
@@ -504,8 +523,9 @@ <h2 id="conclusion">Conclusion</h2>
 Theory.”</span> <em>Physics Reports</em> 666: 1–109.
 </div>
 <div id="ref-cotton2024" class="csl-entry" role="listitem">
-Cotton, Peter. 2024. <span>“Schur Complementary Portfolios.”</span>
-<em>arXiv Preprint arXiv:2411.05807</em>.
+Cotton, Peter. 2024. <span>“Schur Complementary Allocation: A
+Unification of Hierarchical Risk Parity and Minimum Variance
+Portfolios.”</span> <em>arXiv Preprint arXiv:2411.05807</em>.
 </div>
 <div id="ref-james1961" class="csl-entry" role="listitem">
 James, W., and Charles Stein. 1961. <span>“Estimation with Quadratic

papers/refs.bib

@@ -48,7 +48,7 @@ @techreport{antonov2024
 
 @article{cotton2024,
   author  = {Cotton, Peter},
-  title   = {Schur Complementary Portfolios},
+  title   = {Schur Complementary Allocation: A Unification of Hierarchical Risk Parity and Minimum Variance Portfolios},
   journal = {arXiv preprint arXiv:2411.05807},
   year    = {2024}
 }
@@ -235,3 +235,22 @@ @misc{cotton2025psl
   year   = {2025},
   note   = {Note, \texttt{microprediction/precise}}
 }
+
+@article{schafer2005,
+  author  = {Sch\"afer, Juliane and Strimmer, Korbinian},
+  title   = {A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics},
+  journal = {Statistical Applications in Genetics and Molecular Biology},
+  volume  = {4},
+  number  = {1},
+  pages   = {Article 32},
+  year    = {2005}
+}
+
+@misc{cotton2022,
+  author       = {Cotton, Peter},
+  title        = {Schur Complementary Portfolios: A Unification of Machine Learning and Optimization-Based Allocation},
+  year         = {2022},
+  month        = nov,
+  howpublished = {Geek Culture (Medium)},
+  note         = {\url{https://medium.com/geekculture/schur-complementary-portfolios-fix-hierarchical-risk-parity-28b0efa1f35f}}
+}

papers/schur_likelihood_paper.tex

@@ -35,6 +35,19 @@
 lower out-of-sample portfolio variance once the dimension rivals the sample size.
 \end{abstract}
 
+\begin{quote}\small\emph{Note (added 2026, retained as a historical record).} The held-out-likelihood-versus-Schur
+\emph{selection} contrast of Sections~4--5 does not survive scrutiny. In controlled follow-up
+experiments the full likelihood's poor showing there is an artifact of judging by portfolio
+\emph{variance} rather than by likelihood (objective mismatch), not a failure of the likelihood as a
+criterion: restricted to well-conditioned candidates and judged on its own terms it is in fact the
+better selector, and---contrary to a suspicion we briefly held---it does not select ill-conditioned
+estimates (the held-out likelihood penalises them). Two further corrections: the Schur--Ledoit--Wolf
+estimator of Section~6, as implemented, is cross-block \emph{entry} shrinkage (a Sch\"afer--Strimmer-style
+operation), not the structured Schur damping it is named for; and that structured damping is viable only
+with a regularised hedge. The durable contributions are the closed-form reliability $\gamma^\star$
+(Section~3) and the estimator family. See the companion note \emph{Two Sides of Schur Damping} for the
+corrected and unified account.\end{quote}
+
 \section{The high-dimensional failure of the Gaussian likelihood}
 A correlation matrix is the hard part of a covariance matrix: variances are a one-dimensional,
 per-series problem, while the high-dimensional difficulty---the near-singular spectrum and the unstable