geotoolsR (version 1.1)

gboot_cross: Cross-validation bootstrap

Description

Performs a boostrap based on error from the cross-validation

Usage

gboot_cross(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).

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.

Details

We can define the error of prediction by \(\epsilon({s_i})=Z({s_i})-\hat Z({s_i})\), where \(\hat Z({s_i})\) are obtained from cross-validation. The steps of the algorithm are:

1. Set \({s_i}^*={s_i}\);

2. Obtain \(\hat Z({s_i})\) from \(\hat Z({s_i})=\sum\limits_{j \ne i}^{n - 1}{{\lambda _j}Z({s_j})}\);

3. Calculate \(\epsilon({s_i})=Z({s_i})-\hat Z({s_i})\)

4. Sample with replacement \(\epsilon^*(s_i)\) from \(\epsilon (s_i) - \bar \epsilon (s_i)\);

5. The new data will be \(Z^*({s_i})=\hat Z({s_i})+ \epsilon^*(s_i)\);

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.

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_cross(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

# 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_cross(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
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