This package implements nonparametric methods for inference on multidimensional spatial (or spatio-temporal) processes, which may be (especially) useful in (automatic) geostatistical modeling and interpolation.

Main functions

Nonparametric methods for inference on both spatial trend and variogram functions:

np.fitgeo (automatically) fits an isotropic nonparametric geostatistical model by estimating the trend and the variogram (using a bias-corrected estimator) iteratively (by calling, locpol, np.svariso.corr and at each iteration).

locpol, np.den and np.svar use local polynomial kernel methods to compute nonparametric estimates of a multidimensional regression function, a probability density function or a semivariogram (or their first derivatives), respectively. Estimates of these functions can be constructed for any dimension (the amount of available memory is the only limitation). To speed up computations, linear binning is used to discretize the data. A full bandwidth matrix and a multiplicative triweight kernel is used to compute the weights. Main calculations are performed in FORTRAN using the LAPACK library.

np.svariso.corr computes a bias-corrected nonparametric semivariogram estimate using an iterative algorithm similar to that described in Fernandez-Casal and Francisco-Fernandez (2014). This procedure tries to correct the bias due to the direct use of residuals, obtained from a nonparametric estimation of the trend function, in semivariogram estimation. fits a `nonparametric' isotropic Shapiro-Botha variogram model by WLS. Currently, only isotropic semivariogram estimation is supported.

Nonparametric residual kriging (sometimes called external drift kriging):

np.kriging computes residual kriging predictions (and the corresponding simple kriging standard errors).

kriging.simple computes simple kriging predictions, standard errors

Currently, only global simple kriging is implemented in this package. Users are encouraged to use krige (or utilities in gstat package together with as.vgm for local kriging.

Other functions

Among the other functions intended for direct access by the user, the following (methods for multidimensional linear binning, local polynomial kernel regression, density or variogram estimation) could be emphasized: binning, bin.den, svar.bin, and interp.

There are functions for plotting data joint with a legend representing a continuous color scale. splot allows to combine a standard R plot with a legend. spoints, simage and spersp draw the corresponding high-level plot with a legend strip for the color scale. These functions are based on image.plot of package fields.

There are also some functions which can be used to interact with other packages. For instance, as.variogram (geoR) or as.vgm (gstat).


Important suggestions and contributions to some techniques included here were made by Sergio Castillo-Paez (Universidad de las Fuerzas Armadas ESPE, Ecuador) and Tomas Cotos-Ya\~nez (Dep. Statistics, University of Vigo, Spain).


Castillo-Páez S., Fernández-Casal R. and García-Soidán P. (2019) A nonparametric bootstrap method for spatial data, 137, Comput. Stat. Data Anal., 1-15, doi: 10.1016/j.csda.2019.01.017 .

Fernandez-Casal R., Castillo-Paez S. and Francisco-Fernandez M. (2018) Nonparametric geostatistical risk mapping, Stoch. Environ. Res. Ris. Assess., 32, 675-684, doi: 10.1007/s00477-017-1407-y .

Fernandez-Casal R., Castillo-Paez S. and Garcia-Soidan P. (2017) Nonparametric estimation of the small-scale variability of heteroscedastic spatial processes, Spa. Sta., 22, 358-370, doi: 10.1016/j.spasta.2017.04.001 .

Fernandez-Casal R. and Francisco-Fernandez M. (2014) Nonparametric bias-corrected variogram estimation under non-constant trend, Stoch. Environ. Res. Ris. Assess., 28, 1247-1259, doi: 10.1007/s00477-013-0817-8 .

Fernandez-Casal R., Gonzalez-Manteiga W. and Febrero-Bande M. (2003) Flexible Spatio-Temporal Stationary Variogram Models, Statistics and Computing, 13, 127-136, doi: 10.1023/A:1023204525046 .

Rupert D. and Wand M.P. (1994) Multivariate locally weighted least squares regression. The Annals of Statistics, 22, 1346-1370.

Shapiro A. and Botha J.D. (1991) Variogram fitting with a general class of conditionally non-negative definite functions. Computational Statistics and Data Analysis, 11, 87-96.

Wand M.P. (1994) Fast Computation of Multivariate Kernel Estimators. Journal of Computational and Graphical Statistics, 3, 433-445.

Wand M.P. and Jones M.C. (1995) Kernel Smoothing. Chapman and Hall, London.


Ruben Fernandez-Casal (Dep. Mathematics, University of A Coru\~na, Spain). Please send comments, error reports or suggestions to