jackVarField {boodd}R Documentation

Jackknife Variance for Random Fields Based on Blocks

Description

Estimates the variance of a statistic applied to random fields using non-overlapping multidimensional blocks.

Usage

jackVarField(arr, func, length.block, ...)

Arguments

arr

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

func

The function applied to each bootstrap sample.

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.

...

Optional additional arguments for the func function.

Details

The jackVarField function computes the jackknife variance estimator for random fields. It involves dividing the array into non-overlapping blocks of size specified by length.block and applying the function func, having output size equal to p, to the data with each block removed in turn. Finally, an empirical variance of the obtained values is computed. This method is particularly useful for data with spatial or multidimensional structure.

Value

Returns a scalar or a covariance matrix, depending on whether the function func is univariate or multivariate. For a function returning a vector of length p, the output will be a covariance matrix of size p x p.

References

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

Carlstein, E. (1986). The use of subseries methods for estimating the variance of a general statistic from a stationary time series. Annals of Statist., 14, 1171-1179.

Gray, H., Schucany, W. and Watkins, T. (1972). The Generalized Jackknife Statistics. Marcel Dekker, New York.

Quenouille, M.H. (1949). Approximate tests of correlation in time-series. J. Roy. Statist. Soc., Ser. B, 11, 68-84.

See Also

jackVar, jackFunc, blockboot, jackVarBlock, jackFuncRegen.

Examples

arr <- array(rnorm(1000), dim = c(10, 10, 10))
func <- function(x) { mean(x) }
length.block <- c(2, 2, 2)
result <- jackVarField(arr, func, length.block) 

[Package boodd version 0.1 Index]