# np.svar: Local polynomial estimation of the semivariogram In npsp: Nonparametric Spatial Statistics

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```np.svar(x, ...) ## Default S3 method: 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 class '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("ARSE", "ARAE", "ASE", "AAE"), 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, 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. `ylim` y-limits of the plot (if `plot == TRUE`).

## 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.

## 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.

## 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`.