ESTIMATING THE SMOOTHNESS OF A GAUSSIAN RANDOM FIELD FROM IRREGULARLY SPACED DATA VIA HIGHER-ORDER QUADRATIC VARIATIONS

• 成果类型: Article
• 署名作者: Loh, Wei-Liem
• 署名单位: National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1365
• 发表日期: 2015
• 页码: 2766-2794
• 关键词: fractal dimension

摘要

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of the corresponding fixed-domain asymptotic theory. In particular, we consider: (i) higher-order quadratic variations using nonequispaced line transect data, (ii) second-order quadratic variations from a sample of Gaussian random field observations taken along a smooth curve in R-2, (iii) second-order quadratic variations based on deformed lattice data on R-2. Smoothness estimators are proposed that are strongly consistent under mild assumptions. Simulations indicate that these estimators perform well for moderate sample sizes.