Nonstationary positive definite tapering on the plane

Ethan Anderes, Raphaël Huser, Douglas Nychka, Andmarc Coram

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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
Issue number4
StatePublished - 2013


  • Covariance tapering
  • Kriging
  • Optimization
  • Random fields

ASJC Scopus subject areas

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


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