Krige, smooth, both or neither? (with Discussion)

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Both kriging and non-parametric regression smoothing can model a non-stationary regression function with spatially correlated errors. However comparisons have mainly been based on ordinary kriging and smoothing with uncorrelated errors. Ordinary kriging attributes smoothness of the response to spatial autocorrelation whereas non-parametric regression attributes trends to a smooth regression function. For spatial processes it is reasonable to suppose that the response is due to both trend and autocorrelation. This paper reviews methodology for non-parametric regression with autocorrelated errors which is a natural compromise between the two methods. Re-analysis of the one-dimensional stationary spatial data of Laslett (1994) and a clearly non-stationary time series demonstrates the rather surprising result that for these data, ordinary kriging outperforms more computationally intensive models including both universal kriging and correlated splines for spatial prediction. For estimating the regression function, non-parametric regression provides adaptive estimation, but the autocorrelation must be accounted for in selecting the smoothing parameter.

Original languageEnglish (US)
Pages (from-to)441-461
Number of pages21
JournalAustralian and New Zealand Journal of Statistics
Volume42
Issue number4
DOIs
StatePublished - Jan 1 2000

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Ordinary Kriging
Nonparametric Regression
Regression Function
Autocorrelation
Smoothing
Universal Kriging
Attribute
Spatial Prediction
Spatial Autocorrelation
Correlated Errors
Non-stationary Time Series
Regression Estimation
Spatial Process
Adaptive Estimation
Smoothing Parameter
Kriging
Spatial Data
Smooth function
Spline
Smoothness

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Krige, smooth, both or neither? (with Discussion). / Altman, Naomi S.

In: Australian and New Zealand Journal of Statistics, Vol. 42, No. 4, 01.01.2000, p. 441-461.

Research output: Contribution to journalArticle

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