The Annals of Statistics

Local intrinsic stationarity and its inference

Tailen Hsing, Thomas Brown, and Brian Thelen

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Intrinsic random functions nonparametric estimation nonstationary spatial process


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.

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