Helpers for the method by Boos and Zhang (2000) for estimating rejection rate for resampling-based tests.
Usage
Rs_bz_supported(
alpha = 0.05,
Rmax = getOption("power4mome.bz_Rmax", default = 359)
)
R_for_bz(R_target, alpha = 0.05)Arguments
- alpha
The level of significance, two-tailed.
- Rmax
The maximum number of resamples to be returned. Default is 359. Though it is possible to use 1999 resamples or even more with Boos-Zhang-2000, using such a large number of resamples defeats the goal to reduce processing time.
- R_target
The target maximum number of resamples.
Value
The function Rs_bz_supported() returns
a numeric vector of the numbers of
resamples supported.
The function R_for_bz() returns
a scalar.
Details
Boos and Zhang (2000) proposed
a method to estimate the rejection
rate (power, if the null hypothesis is false)
for methods based on resampling, such
as nonparametric bootstrapping. This
method is used by some functions
in power4mome, such as x_from_power().
This method is implemented internally. Some helper functions regarding this method is exported for users.
The function Rs_bz_supported() returns
the number of bootstrap samples (for bootstrapping)
or simulated samples (for Monte Carlo),
both called resamples below for brevity,
usually specified by the argument R,
that can be
used for the Boos-Zhang-2000 method,
given the desired two-tailed level of significance,
(.05 by default).
If possible, setting the number of resamples.
(e.g., setting R when calling x_from_power())
will automatically enable the Boos-Zhang-2000
method (unless explicitly turned off
by setting the option "power4mome.bz"
to FALSE by options("power4mome.bz") <- FALSE),
substantially reducing the processing
time. For now, only two-tailed tests are supported.
Given a target maximum number of
resamples and a level of significance,
the function R_for_bz() returns
largest number of resamples that can be
used for the Boos-Zhang-2000 method.
This function can be used for
arguments such as R in x_from_power()
to automatically find the largest
value supported by the Boos-Zhang-2000
method.
References
Boos, D. D., & Zhang, J. (2000). Monte Carlo evaluation of resampling-based hypothesis tests. Journal of the American Statistical Association, 95(450), 486–492. doi:10.1080/01621459.2000.10474226