2025/10/23 by Nicholas G. Polson, Daniel Zantedeschi, Polson, Nicholas G. +1 · 1 citation
Computer Science · Mathematics · #Asymptotic distribution #Bayesian probability #Constraint (computer-aided design) #Constructive #Empirical likelihood #Estimator #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Markov Chains and Monte Carlo Methods #Moment (physics) #Probabilistic logic #math.ST #msc:60F10 #msc:62B15 #msc:62C10 #msc:62F15 #stat.TH
paper · pdf · doi:10.48550/arxiv.2510.20742
published in arXiv (Cornell University) (Cornell University) · 42 pages, 7 external figure files. Main text and appendix combined. v4 aligns the preprint with corrected fixed-chart localization assumptions and constants, strengthened refinement hypotheses, added an exact finite-chart collapse calculation and updated the partition-sizing calibration; reference metadata, estimator terminology, and source attributions were also checked and corrected
openalex publication_date 2025/10/23 · openalex created_date 2025/10/25 · arxiv created 2026/07/28 · arxiv updated 2026/07/30 · openalex updated_date 2026/08/05
Moment restrictions specify a class of laws, not a predictive model. We obtain one by conditioning an independent sample from a reference law on its empirical moments, and define prediction as the law of a fixed block selected from that conditioned ensemble. On a finite partition this law is an exact mixture over empirical types. Under exact feasibility and lattice regularity, the mixing law has a Gaussian limit on the feasible tangent space, governed by the reduced Hessian, and the selected block approaches independent sampling from the Kullback-Leibler projection. A separate finite-sample bound gives the same product limit for general real-valued restrictions without lattice assumptions. Refinement recovers the projection on the original sample space. Parameterizing the projected family produces a predictive product criterion with a local inverse-covariance expansion, connecting the construction to generalized method of moments.