fieldbootP {boodd}R Documentation

Bootstrap Sample from the Random Field

Description

Function returns a bootstrap sample of the random field on a lattice, using various block bootstrap methods such as moving block, circular block, or nonoverlapping block bootstrap.

Usage

fieldbootP(
  arr,
  length.block,
  method = c("movingblock", "nonoverlapping", "circular")
)

Arguments

arr

A multidimensional real-valued array; it represents a random field on a grid of dimension equals to dimension of the arr.

length.block

An integer or vector of integers; it specified the block lengths for blocks. If a scalar is provided, the same block length is used for all dimensions.

method

The method for array reconstruction:

  • "movingblock" - Moving Block Bootstrap,

  • "nonoverlapping" - Nonoverlapping Block Bootstrap,

  • "circular" - Circular Block Bootstrap (obtained by wrapping the field on the torus). Default is "movingblock".

Details

In the case of random fields, the blocks B_{i}'s are random matrices of size length.block. From the set of all blocks \mathcal{B}=\{B_{1},B_{2},\dots,B_{q}\}, we select randomly with replacement blocks B_{1}^{\ast},\dots,B_{l}^{\ast} and bind them together. The probability of choosing any block is 1/q.

Value

Returns a bootstrap sample of given arr.

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Bertail, P. Politis, D. N. Rhomari, N. (2000). Subsampling continuous parameter random fields and a Bernstein inequality, Statistics, 33, 367-392.

Nordman, D.J. Lahiri, S.N.(2004). On optimal spatial subsample size for variance estimation, The Annals of Statistics, 32, 1981-2027.

Politis, D.N. Romano, J.P. (1993). Nonparametric Resampling for Homogeneous Strong Mixing Random Fields, J. Multivar. Anal., 47, 301-328.

See Also

blockboot, jackVarField, field.sub, fieldboot.

Examples


library(geoR)
N=10
n=N^2
sim <- grf(n, grid="reg", cov.pars=c(1, .25), nsim=1)
image(sim) 
arr=array(sim$data,dim=c(N,N))
mb=fieldbootP(arr,length.block=c(2,2),method="movingblock")
simb=sim
simb$data=as.vector(mb)
image(simb)


[Package boodd version 0.1 Index]