Variogram estimation in the presence of trend

Nikolay Bliznyuk, Raymond J. Carroll, Marc G. Genton*, Yuedong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Estimation of covariance function parameters of the error process in the presence of an unknown smooth trend is an important problem because solving it allows one to estimate the trend nonparametrically using a smoother corrected for dependence in the errors. Our work is motivated by spatial statistics but is applicable to other contexts where the dimension of the index set can exceed one. We obtain an estimator of the covariance function parameters by regressing squared differences of the response on their expectations, which equal the variogram plus an offset term induced by the trend. Existing estimators that ignore the trend produce bias in the estimates of the variogram parameters, which our procedure corrects for. Our estimator can be justified asymptotically under the increasing domain framework. Simulation studies suggest that our estimator compares favorably with those in the current literature while making less restrictive assumptions. We use our method to estimate the variogram parameters of the short-range spatial process in a U.S. precipitation data set.

Original languageEnglish (US)
Pages (from-to)159-168
Number of pages10
JournalStatistics and its Interface
Issue number2
StatePublished - 2012


  • Bias
  • Covariance function
  • Nonlinear regression
  • Nonparametric regression
  • Spatio-temporal dependence
  • Time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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