best.sub.size.iid {boodd}R Documentation

Optimal Block Subsampling or MOON Bootstrap Sizes for I.I.D. Data

Description

This function determines the optimal block size for subsampling or moon bootstrap sizes using a distance-based method, specifically applying undersampling techniques for independent and identically distributed (i.i.d.) data. It computes Kolmogorov distances between consecutive subsampling (or moon bootstrap) distributions to select the most suitable block size.

Usage

best.sub.size.iid(X, func, B = 999, PLT = TRUE, qq = 0.75, rep = FALSE, ...)

Arguments

X

A numeric vector or data representing i.i.d. observations.

func

A function pplied to the blocks.

B

An integer; the number of resampling replications. Default is 999.

PLT

Logical. If TRUE (default), plots the Kolmogorov distances versus subsampling sizes and intermediate regression results.

qq

A numeric value in the interval (0, 1). Determines the scaling factor for subsampling sizes. Higher values result in more subsampling distributions being computed. Default is 0.75.

rep

Logical. If TRUE, performs moon bootstrap (subsampling with replacement). If FALSE (default), performs subsampling without replacement.

...

Optional additional arguments passed to the func function.

Details

This function implements a procedure based on the method proposed by Götze and Račkauskas (2001) and Bickel and Sakov (2008) for determining optimal subsampling sizes in i.i.d. case. It computes a range of subsampling distributions or moon bootstrap distribution for sizes proportional to powers of qq. The function then evaluates the Kolmogorov distance between consecutive distributions. The optimal block size is the value which minimises this distance.

Sometimes looking at the plot is more informative, especially when the distance does not vary very much. In this case, the largest value in a stable zone will be a better choice than the minimiser of the distance.

Value

Returns the optimal block size for subsampling or moon bootstrap.

References

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

Bickel, P., and Sakov, A. (2008). On the choice of m in the m out of n bootstrap and confidence bounds for extrema. Statistica Sinica, 18 967–985.

Götze, F. and Račkauskas, A. (2001). Adaptive choice of bootstrap sample sizes. In State of the art in probability and statistics. Institute of Mathematical Statistics, pp. 286-310.

See Also

block.sub, rate.sub, rate.block.sub, best.block.sub.size.

Examples

 set.seed(12345)
 n = 1000 # sample size
 ts = rnorm(n)
 bopt=best.sub.size.iid(ts,max)

[Package boodd version 0.1 Index]