# gboot_solow: Solow bootstrap In geotoolsR: Tools to Improve the Use of Geostatistic

## Description

Performs a spatial boostrap proposed by Solow(1985).

## Usage

 1 gboot_solow(data,var,model,B) 

## Arguments

 data object of the class geodata. var object of the class variogram. model object of the class variomodel. B number of the bootstrap that will be performed (default B=1000).

## Details

The basic idea involves transforming correlated observation to uncorrelated quantities, forming a bootstrap sample from these quantities, and transforming back to a bootstrap sample form the original observations (SOLOW, 1985). Suppose that Z_n is an n vector of observations from a realization of a second-order stationary random process, Z(s_i), and the covariance matrix for Z_n is C. Suppose further that E(Z_n)={0_n}, where {0_n} is an n vector of zeroes. In practice Z_n can be centered by subtracting an estimate of the stationary mean from each observation. So, the steps of the algorithm are:

1. Obtain C;

2. Apply the Cholesky decomposition in C, obtaining C=LL^t, where L is lower triangular;

3. Obtain U_n=L^{-1}Z_n;

4. Sample with replacement {U^*}_n from U_n - \bar U_n;

5. The new data will be {Z^*}_n=L{U^*}_n;

6. Calculate the new variogram;

7. Calculate and save the statistics of interest;

8. Return to step 4 and repeat the process at least 1000 times.

## Value

variogram_boot gives the variogram of each bootstrap.

variogram_or gives the original variogram.

pars_boot gives the estimatives of the nugget, sill, contribution, range and practical range for each bootstrap.

pars_or gives the original estimatives of the nugget, sill, contribution, range and practical range.

Invalid arguments will return an error message.

## Author(s)

Diogo Francisco Rossoni dfrossoni@uem.br

Vinicius Basseto Felix felix_prot@hotmail.com

## References

Solow, A. R. (1985). Bootstrapping correlated data. Journal of the International Association for Mathematical Geology, 17(7), 769-775. https://doi.org/10.1007/BF01031616

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 # Example 1 ## transforming the data.frame in an object of class geodata data<- as.geodata(soilmoisture) points(data) ## data visualization var<- variog(data, max.dist = 140) ## Obtaining the variogram plot(var) ## Fitting the model mod<- variofit(var,ini.cov.pars = c(2,80),nugget = 2,cov.model = "sph") lines(mod, col=2, lwd=2) ##fitted model ## Bootstrap procedure boot<- gboot_solow(data,var,mod,B=10) ## For better Confidence interval, try B=1000 gboot_CI(boot,digits = 4) ## Bootstrap Confidence Interval gboot_plot(boot) ## Bootstrap Variogram plot ## Not run: # Example 2 ## transforming the data.frame in an object of class geodata data<- as.geodata(NVDI) points(data) ## data visualization var<- variog(data, max.dist = 18) ## Obtaining the variogram plot(var) ## Fitting the model mod<- variofit(var,ini.cov.pars = c(0.003,6),nugget = 0.003,cov.model = "gaus") lines(mod, col=2, lwd=2) ##fitted model ## Bootstrap procedure boot<- gboot_solow(data,var,mod,B=10) ## For better Confidence interval, try B=1000 gboot_CI(boot,digits = 4) ## Bootstrap Confidence Interval gboot_plot(boot) ## Bootstrap Variogram plot ## End(Not run) 

geotoolsR documentation built on March 2, 2020, 5:07 p.m.