## The Annals of Statistics

### Local intrinsic stationarity and its inference

#### 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
Revised: September 2015
First available in Project Euclid: 12 September 2016

https://projecteuclid.org/euclid.aos/1473685268

Digital Object Identifier
doi:10.1214/15-AOS1402

Mathematical Reviews number (MathSciNet)
MR3546443

Zentralblatt MATH identifier
1360.62475

#### 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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