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.
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.
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