jackFuncBlock {boodd}R Documentation

Jackknife Variance Function Using Blocks of Fixed Length

Description

Creates a vector-valued function for computing both the statistic defined by func and the estimated jackknife variance based on the blocks.

Usage

jackFuncBlock(func, length.block = NULL, ...)

Arguments

func

The function used to compute the statistic on each sample.

length.block

An integer; the block length. If not provided, a default value equals \lfloor\left(length(X)\right)^{\frac{1}{3}}\rfloor.

...

Optional additional arguments for the func function.

Details

The jackFuncBlock function constructs a new function that, when applied to a data sample, calculates both the statistic specified by func and its associated jackknife variance based on non-overlapping blocks of fixed length equals to length.block.

The block jackknife method is an extension of the jackknife resampling technique, used to estimate the bias and variance of a statistical estimate in the presence of dependent data.

Value

Returns an object which is a function.

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

# Create a function to compute the empirical skewness
func <- function(x) { mean((x - mean(x))^3) / (mean((x - mean(x))^2)^(3/2)) }
x <- arima.sim(list(order = c(1, 0, 4), ar = 0.5, ma = c(0.7, 0.4, -0.3, -0.1)), n = 100)
# Create a function to compute the empirical skewness and its variance based on blocks of size 5
jfb <- jackFuncBlock(func, length.block = 5)
# Bootstrapping of the skewness and its variance allows to construct 
# bootstrap-t confidence intervals
boo2 <- blockboot(x, jfb, 299, length.block=7, method="circular")
confint(boo2, method="all")

[Package boodd version 0.1 Index]