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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Cauchy Aggregation of Ridge-Regularized Hotelling Tests f...
[Submitted on 12 Jun 2026] · 2026-06-15 · via stat updates on arXiv.org

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Abstract:Ridge-regularized Hotelling-type (RHT) change-point tests depend on a ridge parameter $\lambda$, but the power-optimal value is determined by the unknown covariance structure and the unknown mean shift. We avoid selecting a single ridge value by computing fixed-ridge p-values on a finite deterministic grid and aggregating them with the Cauchy combination rule. Under the standard random-matrix conditions for fixed-ridge RHT statistics, we establish finite-grid joint weak convergence of the ridge processes. This leads to fixed-level validity under joint-limit calibration and small-tail validity for the analytic Cauchy p-value. Monte Carlo experiments show that deterministic-grid Cauchy aggregation has stable size behavior and achieves power close to the best stable fixed ridge choice across a range of covariance and signal configurations.

Submission history

From: Long Feng [view email]
[v1] Fri, 12 Jun 2026 04:14:06 UTC (58 KB)