The Annals of Statistics

Local intrinsic stationarity and its inference

Tailen Hsing, Thomas Brown, and Brian Thelen

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Abstract

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.

Article information

Source
Ann. Statist., Volume 44, Number 5 (2016), 2058-2088.

Dates
Received: October 2014
Revised: September 2015
First available in Project Euclid: 12 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1473685268

Digital Object Identifier
doi:10.1214/15-AOS1402

Mathematical Reviews number (MathSciNet)
MR3546443

Zentralblatt MATH identifier
1360.62475

Subjects
Primary: 60G12: General second-order processes 62M30: Spatial processes 62G05: Estimation 62G20: Asymptotic properties

Keywords
Intrinsic random functions nonparametric estimation nonstationary spatial process

Citation

Hsing, Tailen; Brown, Thomas; Thelen, Brian. Local intrinsic stationarity and its inference. Ann. Statist. 44 (2016), no. 5, 2058--2088. doi:10.1214/15-AOS1402. https://projecteuclid.org/euclid.aos/1473685268


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