On identifiability and consistency of the nugget in Gaussian spatial process models

• 成果类型: Article
• 署名作者: Tang, Wenpin; Zhang, Lu; Banerjee, Sudipto
• 署名单位: Columbia University; Columbia University; University of California System; University of California Los Angeles
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12472
• 发表日期: 2021
• 页码: 1044-1070
• 关键词: asymptotic properties; random-field; prediction

摘要

Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or microscale variability, and is called the 'nugget'. We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, that is the sample size increases within a sampling domain that is bounded. Our work extends results in fixed domain asymptotics for spatial models without the nugget. More specifically, we establish the identifiability of parameters in the Matern covariogram and the consistency of their maximum likelihood estimators in the presence of discontinuities due to the nugget. We also present simulation studies to demonstrate the role of the identifiable quantities in spatial interpolation.