jackVarBlock {boodd}R Documentation

Jackknife Variance Estimator Based on Fixed Length Blocks

Description

Estimates the variance of a statistic applied to a vector or a matrix using a block jackknife procedure.

Usage

jackVarBlock(x, func, length.block, ...)

Arguments

x

A vector or a matrix representing the data.

func

The function used to compute the statistic on each sample.

length.block

An integer; the block length.

...

Optional additional arguments for the func function.

Details

The jackVarBlock function extends the jackknife variance estimation to block data. The data x is divided into non-overlapping blocks of length length.block. The function func, having output size equal to p, is applied to the data with each block removed in turn to finally compute an empirical variance of the obtained values. This approach is particularly useful for dependent data, where traditional jackknife methods may not be appropriate.

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, jackFuncBlock, jackFuncRegen.

Examples

set.seed(1)
x <- arima.sim(list(order = c(1, 0, 4), ar = 0.5, ma = c(0.7, 0.4, -0.3, -0.1)), n = 101)
# Jackknife variance estimator of 'func' with blocks of length length.block
length.block <- 10
V1 <- jackVarBlock(x, mean, length.block)

[Package boodd version 0.1 Index]