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 |
PLT |
Logical. If |
qq |
A numeric value in the interval |
rep |
Logical. If |
... |
Optional additional arguments passed to the |
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)