Nonstationary positive definite tapering on the plane

Ethan Anderes, Raphael Huser, Douglas Nychka, Andmarc Coram

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

A common problem in spatial statistics is to predict a random field f at some spatial location t0 using observations f (t1),..., f (tn) at t1,..., tn ∈ ℝd. Recent work by Kaufman et al. and Furrer et al. studies the use of tapering for reducing the computational burden associated with likelihood-based estimation and prediction in large spatial datasets. Unfortunately, highly irregular observation locations can present problems for stationary tapers. In particular, there can exist local neighborhoods with too few observations for sufficient accuracy, while others have too many for computational tractability. In this article, we show how to generate nonstationary covariance tapers T (s, t) such that the number of observations in {t: T (s, t) > 0} is approximately a constant function of s. This ensures that tapering neighborhoods do not have too many points to cause computational problems but simultaneously have enough local points for accurate prediction. We focus specifically on tapering in two dimensions where quasiconformal theory can be used. Supplementary materials for the article are available online.

Original languageEnglish (US)
Pages (from-to)848-865
Number of pages18
JournalJournal of Computational and Graphical Statistics
Volume22
Issue number4
DOIs
StatePublished - Jan 1 2013

Keywords

  • Covariance tapering
  • Kriging
  • Optimization
  • Random fields

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics

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