2209.01679
Orthogonal and Linear Regressions and Pencils of Confocal Quadrics
Vladimir Dragović, Borislav Gajić
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves that equal-moment hyperplanes are exactly the tangent hyperplanes to a member of the associated confocal pencil and classifies the envelope; it also shows that, for a point P, the best/worst hyperplanes (and ℓ-planes) through P correspond to tangents at P to the confocal quadrics with extremal Jacobi coordinates, yielding explicit formulas. The candidate solution reaches the same conclusions via a slightly different route: a clean support-function envelope argument for (6.13) and an explicit eigenpair identity J_P v(λ) = (2J1 − m λ) v(λ) together with a Ky Fan-type argument for ℓ-planes. Results and formulas match the paper.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript successfully unifies inertia geometry and confocal quadrics with orthogonal regression problems. Core claims are correct and novel in their cohesive treatment. Some arguments could be tightened (e.g., the mapping among parameters A, μ, λ; explicit eigenvector computations at P), and assumptions made more explicit. The paper is solid and publishable after minor clarifications.