precise projectA Principled Pseudo-Likelihood in High Dimensions · Peter Cotton
The Gaussian log-likelihood fails — below chance — at ranking covariance estimates in high dimensions. We introduce the Schur pseudo-likelihood, a one-parameter family that damps the cross-block coupling of the likelihood through its Schur complements, bridging the full and block-diagonal likelihoods, and derive the optimal coupling strength in closed form.
High-Dimensional Pseudo-Likelihoods and Portfolio Allocation · Peter Cotton
Spatial statisticians fitting high-dimensional weather fields and quantitative investors building portfolios have independently arrived at the same object: a Schur complement damped by one interpretable parameter — a conditional covariance for the statistician, a hedged residual risk for the investor. We show these are one operation, so the closed-form reliability that sets the damping is at once a James–Stein shrinkage and a Ledoit–Wolf intensity, and note what each literature has supplied that the other lacks.
Learning Covariance Eigenvalue Corrections One Observation at a Time · Peter Cotton
Cross-validated covariance cleaning must partition a sample to learn what variance belongs to an empirical eigenvector. In a stream it need not: the basis carried forward from past data is already out of sample with respect to the next observation, so the arrow of time supplies the split for free, and every observation labels every eigenvalue at once. We give the conditional identity and the exact Frobenius decomposition behind it, a one-pass estimator costing O(p²) per observation, and the result we did not expect: the learned correction is beaten, wherever dependence drifts, by putting the analytical map on a rolling window.
Interactive companions to the papers
How the methods relate to neighboring research, drawn as graphs — solid edges are established connections, dashed red edges are verified absences: the research directions. First map: Schur Damping: Research Directions.
The web editions are generated from their LaTeX sources
(docs/build_paper.sh), so they never drift from the PDF.