fieldboot {boodd}R Documentation

Block Bootstrap of Random Field

Description

Performs a bootstrap analysis of multidimensional array representing a random field on a lattice, using various block bootstrap methods such as moving block, circular block, or nonoverlapping block bootstrap.

Usage

fieldboot(
  arr,
  func,
  B,
  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.

func

The function applied to each bootstrap sample.

B

A positive integer; the number of bootstrap samples.

length.block

A positive 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.

...

Optional additional arguments for the func function.

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

The fieldboot function resamples hyper-rectangles constructed using either moving blocks, nonoverlapping blocks or circular blocks to construct a bootstrap field of the same dimension as the original one. Then it applies the specified func to bootstrap samples of the provided data array. The length.block parameter determines the size of the blocks used in the bootstrap method. The method parameter specifies the type of block bootstrap to use. This function is useful for assessing the variability and distribution properties of a statistic in the context of random fields.

Value

Returns an object of class boodd.

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, fieldbootP.

Examples


set.seed(123)
arr <- array(rnorm(1000), dim = c(10, 10, 10))
res <- fieldboot(arr, mean, B = 100, length.block = c(2, 2, 2))
plot(res)


[Package boodd version 0.1 Index]