jackVar {boodd}R Documentation

Jackknife Variance Estimator

Description

Estimates the variance of a statistic using the jackknife-variance procedure in the i.i.d case.

Usage

jackVar(x, func, ...)

Arguments

x

A vector or a matrix representing the data.

func

The function used to compute the statistic on each sample.

...

Optional additional arguments for the func function.

Details

When x is a vector of length n or a matrix with n rows, the function func, having output size equal to p, is applied to x with each i-th row removed, resulting in

T_{n-1}^{i} = func(x[-i]).

The jackknife variance is computed based on these recalculated statistics and the original statistic

T_n = func(x).

The covariance matrix is calculated according to the jackknife formula.

This method is used to estimate the variance of a statistic that is potentially biased due to the finite sample size.

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.

Efron, B. (1979). Bootstrap methods: another look at the jackknife. Ann. Statist., 7, 1-26.

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

jackFunc, boots, jackVarBlock, jackFuncBlock, jackFuncRegen.

Examples

set.seed(1)
x <- rnorm(101)
func <- function(x) { mean(x^2) }
jackVar(x, func)
# Function returning a vector with the mean and standard deviation of x
mfunc <- function(x) { c(mean(x), sd(x)) }
jackVar(x, mfunc)
# Function to compute the moment of order p with p as additional argument
funca <- function(x, p) { mean((x-mean(x))^p)}
jackVar(x, funca, 3)

[Package boodd version 0.1 Index]