gboot_solow: Solow bootstrap

Description Usage Arguments Details Value Author(s) References Examples

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 [email protected]

Vinicius Basseto Felix [email protected]

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

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# 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 May 2, 2019, 5:51 a.m.