rate.block.sub {boodd}R Documentation

Block Subsampling for Time Series with Convergence Rate Estimation

Description

Performs block subsampling for a time series 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.block.sub(X, func, n_b = 99, q = 0.75, PLT = TRUE, ...)

Arguments

X

A numeric vector or a time series.

func

The function to be estimated using block subsampling.

n_b

A positive integer; the number of subsampling distributions to be constructed, with block 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.sub performs block subsampling, specifically suited for time series 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. Journal of the American Statistical Association, 94, 569-579.

See Also

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

Examples

set.seed(12345)
n = 500 # sample size
ts = arima.sim(n=n,model=list(ar=c(0.4)))*sqrt(1-0.4^2) # Generating an AR(1) 
# process with variance 1
# Moon MBB without replacement with estimated rate
reb=rate.block.sub(ts,mean,PLT=TRUE)

[Package boodd version 0.1 Index]