STATISTICAL INFERENCE FOR SPATIAL STATISTICS DEFINED IN THE FOURIER DOMAIN

• 成果类型: Article
• 署名作者: Rao, Suhasini Subba
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1556
• 发表日期: 2018
• 页码: 469-499
• 关键词: CENTRAL-LIMIT-THEOREM; time-series; parameter-estimation; quadratic-forms; CONVERGENCE; likelihood; variables

摘要

A class of Fourier based statistics for irregular spaced spatial data is introduced. Examples include the Whittle likelihood, a parametric estimator of the covariance function based on the L-2-contrast function and a simple nonparametric estimator of the spatial autocovariance which is a nonnegative function. The Fourier based statistic is a quadratic form of a discrete Fourier-type transform of the spatial data. Evaluation of the statistic is computationally tractable, requiring O(nb) operations, where b are the number of Fourier frequencies used in the definition of the statistic and n is the sample size. The asymptotic sampling properties of the statistic are derived using both increasing domain and fixed-domain spatial asymptotics. These results are used to construct a statistic which is asymptotically pivotal.