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Theory & Methods: Krige, Smooth, Both or Neither?
Author(s) -
Altman Naomi
Publication year - 2000
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00141
Subject(s) - kriging , autocorrelation , mathematics , smoothing , smoothness , spatial analysis , statistics , parametric statistics , ordinary least squares , variogram , nonparametric regression , regression , regression analysis , econometrics , polynomial regression , mathematical analysis
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.