In CAT(0) spaces and for small-enough quadruples of CAT(kappa) spaces, the symmetric trapezoid is shown to be the exact extremal configuration for every transformed-distance inequality indexed by nondecreasing convex functions with concave derivative.
Challenging the empirical mean and the empirical variance: A deviation study
8 Pith papers cite this work, alongside 279 external citations. Polarity classification is still indexing.
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Convex block M-estimators are limited to the median-of-means robustness constant, but nonconvex block-Lp estimators can approach the trimmed-block oracle constant as p goes to 0 under good/bad block separation.
A quotient-affine Riemannian Gaussian on full-rank correlation matrices has finite moments, exact p=2/Fisher likelihood, and a center-dependent normalizer for p=3 that separates MLE from Fréchet estimation.
For mean-zero unit-variance random variables with fourth moment at most κ, the sharp one-sided tail V₁(t,κ) is completely mapped into four explicit regimes, with matching certificates and a proof-degree phase transition.
A general class of shrinkage-based robust mean estimators is shown to attain near-optimal sub-Gaussian concentration whenever the base estimator has bounded error and is computed on an independent sample.
HELPI is a hyperbolic latent position model for binary bipartite data whose identified geometric target is the root-invariant projected Gromov product, with contraction theory and variational computation.
HOMER replaces the geometric median in median-of-means with a radial Huber center, giving heavy-tail robustness and threshold-controlled mean inference in Hilbert spaces.
Statsformer adaptively integrates LLM semantic priors into a library of predictors via out-of-fold validation, delivering an oracle-style guarantee that the final predictor performs no worse than the best convex combination of its candidates up to statistical error.
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Learning When to Trust LLM Priors: A Validated Framework for Semantic Prior Integration
Statsformer adaptively integrates LLM semantic priors into a library of predictors via out-of-fold validation, delivering an oracle-style guarantee that the final predictor performs no worse than the best convex combination of its candidates up to statistical error.