Estimates a multidimensional semivariogram (and its first derivatives) using local polynomial kernel smoothing of linearly binned semivariances.

np.svar(x, ...)

# S3 method for default
np.svar(
x,
y,
h = NULL,
maxlag = NULL,
nlags = NULL,
minlag = maxlag/nlags,
degree = 1,
drv = FALSE,
hat.bin = TRUE,
ncv = 0,
...
)

# S3 method for svar.bin
np.svar(x, h = NULL, degree = 1, drv = FALSE, hat.bin = TRUE, ncv = 0, ...)

np.svariso(
x,
y,
h = NULL,
maxlag = NULL,
nlags = NULL,
minlag = maxlag/nlags,
degree = 1,
drv = FALSE,
hat.bin = TRUE,
ncv = 0,
...
)

np.svariso.hcv(
x,
y,
maxlag = NULL,
nlags = NULL,
minlag = maxlag/nlags,
degree = 1,
drv = FALSE,
hat.bin = TRUE,
loss = c("MRSE", "MRAE", "MSE", "MAE"),
ncv = 1,
warn = FALSE,
...
)

np.svariso.corr(
lp,
x = lp$data$x,
h = NULL,
maxlag = NULL,
nlags = NULL,
minlag = maxlag/nlags,
degree = 1,
drv = FALSE,
hat.bin = TRUE,
tol = 0.05,
max.iter = 10,
plot = FALSE,
verbose = plot,
ylim = c(0, 2 * max(svar\$biny, na.rm = TRUE))
)

## Arguments

x

object used to select a method. Usually a matrix with the coordinates of the data locations (columns correspond with dimensions and rows with data).

...

further arguments passed to or from other methods.

y

vector of data (response variable).

h

(full) bandwidth matrix (controls the degree of smoothing; only the upper triangular part of h is used).

maxlag

maximum lag. Defaults to 55% of largest lag.

nlags

number of lags. Defaults to 101.

minlag

minimun lag.

degree

degree of the local polynomial used. Defaults to 1 (local linear estimation).

drv

logical; if TRUE, the matrix of estimated first derivatives is returned.

hat.bin

logical; if TRUE, the hat matrix of the binned semivariances is returned.

ncv

integer; determines the number of cells leaved out in each dimension. Defaults to 0 (the full data is used) and it is not normally changed by the user in this setting. See "Details" below.

loss

character; CV error. See "Details" bellow.

warn

logical; sets the handling of warning messages (normally due to the lack of data in some neighborhoods). If FALSE all warnings are ignored.

lp

local polynomial estimate of the trend function (object of class locpol.bin).

tol

convergence tolerance. The algorithm stops if the average of the relative squared diferences is less than tol. Defaults to 0.04.

max.iter

maximum number of iterations. Defaults to 10.

plot

logical; if TRUE, the estimates obtained at each iteration are plotted.

verbose

logical; if TRUE, the errors (averages of the relative squared differences) at each iteration are printed.

ylim

y-limits of the plot (if plot == TRUE).

## Value

Returns an S3 object of class np.svar (locpol svar + binned svar + grid par.), extends svar.bin, with the additional (some optional) 3 components:

est

vector or array with the local polynomial semivariogram estimates.

locpol

a list of 6 components:

• degree degree of the local polinomial used.

• h smoothing matrix.

• rm mean of residual semivariances.

• rss sum of squared residual semivariances.

• ncv number of cells ignored in each direction.

• hat (if requested) hat matrix of the binned semivariances.

• nrl0 (if appropriate) number of cells with binw > 0 and est == NA.

deriv

(if requested) matrix of estimated first semivariogram derivatives.

## Details

Currently, only isotropic semivariogram estimation is supported.

If parameter nlags is not specified is set to 101.

The computation of the hat matrix of the binned semivariances (hat.bin = TRUE) allows for the computation of approximated estimation variances (e.g. in fitsvar.sb.iso).

A multiplicative triweight kernel is used to compute the weights.

np.svariso.hcv calls h.cv to obtain an "optimal" bandwith (additional arguments ... are passed to this function). Argument ncv is only used here at the bandwith selection stage (estimation is done with all the data).

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 in this case from a nonparametric estimation of the trend function) in semivariogram estimation.

## References

Fernandez Casal R., Gonzalez Manteiga W. and Febrero Bande M. (2003) Space-time dependency modeling using general classes of flexible stationary variogram models, J. Geophys. Res., 108, 8779, doi:10.1029/2002JD002909 .

Garcia-Soidan P.H., Gonzalez-Manteiga W. and Febrero-Bande M. (2003) Local linear regression estimation of the variogram, Stat. Prob. Lett., 64, 169-179.

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.

svar.bin, data.grid, locpol.