rate.sub {boodd}R Documentation

Subsampling for i.i.d. Data with Convergence Rate Estimation

Description

Performs subsampling for an i.i.d. data with an estimation of the convergence rate of a given statistic. The function constructs subsampling distributions of specified sizes, estimates the convergence rate and asymptotic bias, and provides optional diagnostic plots.

Usage

rate.sub(X, func, B = 999, n_b = 99, q = 0.75, PLT = TRUE, ...)

Arguments

X

A numeric vector.

func

The function to be estimated using subsampling.

B

A positive integer; the number of subsampling replications.

n_b

A positive integer; the number of subsampling distributions to be constructed, with subsampling sizes ranging from \lfloor n^{1/3}\rfloor to \rfloor n^{3/4}\rfloor, where n is the sample size.

q

A numeric value in the interval (0.5, 1); it is used to calculate the interquantile range which estimates the rate of convergence.

PLT

A logical value; By default it is TRUE, plots graphics and intermediate regression results.

...

Additional arguments for the func function.

Details

The function rate.block performs subsampling, specifically suited for i.i.d. data, estimates the convergence rate n^{-\alpha} and the approximation rate n^{-\beta} between the true distribution and the asymptotic one.

Value

A list containing:

alpha

The estimated rate of convergence.

beta

The estimated approximation rate.

obj

An object of class boodd with the optimized subsampling distribution.

References

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

Bertail, P., Politis, D., Romano, J. (1999). On Subsampling Estimators with Unknown Rate of Convergence.

Politis, D. N., Romano, J. P., & Wolf, M. (1999). Subsampling. Springer N.Y..

See Also

rate.block.sub, best.block.sub.size, best.sub.size.iid, block.sub, boots.

Examples

#' set.seed(12345)
n = 500 # sample size
x = rnorm(n)
# Subsampling with estimated rate
reb=rate.sub(x,mean,PLT=TRUE, B=99)

[Package boodd version 0.1 Index]