Work

Infill asymptotics for closed-form alternatives to maximum likelihood estimators of covariance parameters in the Ornstein–Uhlenbeck fields

Year: 2026

Type: article

Abstract: As Gaussian random fields with a Markov property, the Ornstein–Uhlenbeck (OU) fields are widely used to model spatial and temporal dependence in areas such as computer experiments, geostatistics, physics, and finance. This paper considers parameter estimation for the covariance function of a univariate anisotropic OU field on $$\mathbb {R}^d$$ R d for $$d \ge 2$$ d ≥ 2 . Based on observations in a fixed domain, we propose closed-form estimators that eliminate the need for numerical optimization and are computationally more feasible than maximum likelihood estimators. The proposed estimators retain the strong consistency and asymptotic normality, and their asymptotic variances are slightly (at most 14%) larger than those of the MLEs. We provide a simulation study to illustrate the theoretical results in this work.

Source: Annals of the Institute of Statistical Mathematics

DOI: 10.1007/s10463-026-00993-w

Authors: Nian Liu, Haoxiang Feng, Yimin Xiao

Institutions: University of Houston, Minnesota State University, Mankato, Michigan State University

Language: English

Topic: Spatial and Panel Data Analysis

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: hybrid

Funder: National Science Foundation

Award: Analysis and Geometry of Random Fields Related to Stochastic Partial Differential Equations and Random Matrices