LOCAL INTRINSIC STATIONARITY AND ITS INFERENCE

• 成果类型: Article
• 署名作者: Hsing, Tailen; Brown, Thomas; Thelen, Brian
• 署名单位: University of Michigan System; University of Michigan; Exponent
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1402
• 发表日期: 2016
• 页码: 2058-2088
• 关键词: fractional brownian motions; gaussian random-fields; fractal dimension; NONSTATIONARY

摘要

Dense spatial data are commonplace nowadays, and they provide the impetus for addressing nonstationarity in a general way. This paper extends the notion of intrinsic random function by allowing the stationary component of the covariance to vary with spatial location. A nonparametric estimation procedure based on gridded data is introduced for the case where the covariance function is regularly varying at any location. An asymptotic theory is developed for the procedure on a fixed domain by letting the grid size tend to zero.