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 |
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 |
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)