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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
Fast Convergence for Weighted Least Squares Estimates
[Submitted on 30 Apr 2026 (v1), last revised 17 Jul 2026 (this v · 2026-05-01 · via stat updates on arXiv.org

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Abstract:It is well-known that maximum likelihood estimates converge faster than the classic square root rate if the Fisher information is infinite. This is often the case when the effective region depends on the estimated parameters, or when density has a singularity inside the effective region at a point dependent on the estimated parameters. We present a one-parameter family of bivariate absolutely continuous distributions on the half-space with smooth densities. The effective domain is always the same half-space and does not depend on this parameter. The order of magnitude for the weighted least squares estimate is asymptotically smaller than the classic square root rate. For the Gaussian variance mixture case, the maximum likelihood estimate coincides with this weighted least squares estimate.

Submission history

From: Andrey Sarantsev [view email]
[v1] Thu, 30 Apr 2026 20:25:02 UTC (9 KB)
[v2] Wed, 10 Jun 2026 01:22:28 UTC (13 KB)
[v3] Fri, 17 Jul 2026 23:45:17 UTC (13 KB)