mboot.ci {moonboot} | R Documentation |
m-Out-of-n Bootstrap Confidence Intervals
Description
Estimates the confidence interval using the methods provided by types
.
tau
must be a function that calculates teh scaling factor
tau(n) for a given n. If tau
is not provided, it is estimated
with estimate.tau
using the default settings of this function.
Usage
mboot.ci(boot.out, conf = 0.95, tau = NULL, types = "all", ...)
Arguments
boot.out |
The simulated bootstrap distribution from the |
conf |
The confidence level. |
tau |
Function that returns the scaling factor tau in dependence of n. If |
types |
The types of confidence intervals to be calculated. The value can be 'all' for all types, or a
subset of |
... |
When |
Details
As estimating the scaling factor tau(n) can be unreliable, it is recommended
to explicitly provide tau
. Otherwise it is estimated with
estimate.tau
. To specify additional arguments for
estimate.tau
, call this function directly and use its return value
as tau
argument. For the type sherman
, tau
is not
needed and its value is ignored.
The following methods to compute teh confidence intervals are supported
through the parameter type
:
- basic:
-
This method works for all estimators and computes the interval directly from the quantiles of the m-out-of-n bootstrap distribution.
- norm:
-
This method only works for normally distributed estimators. It estimates the variance with the m-out-of-n bootstrap and then computes te interval with the quantiles of teh standard normal distribution.
- sherman:
-
This method does not scale the interval with tau(m)/tau(n) and thus is too wide. To avoid over-coverage, this is compensated by centering it randomly around the point estimators of one of the m-out-of-n bootstrap samples. Although this results on average in the nominal coverage probability, the interval is less accurate than the other intervals and should be used only as a last resort if the scaling factor tau is neither known, nor estimatable.
Value
A list of confidence intervals for the given types.
References
Politis D.N. and Romano J.P. (1994) Large sample confidence regions based on subsamples under minimal assumptions. The Annals of Statistics, 22(4):2031-2050, doi:10.1214/aos/1176325770
Sherman M. and Carlstein E. (2004) Confidence intervals based on estimators with unknown rates of convergence. Computional statistics & data analysis, 46(1):123-136.
Dalitz C. and Lögler M. (2024) moonboot: An R Package Implementing m-out-of-n Bootstrap Methods doi:10.48550/arXiv.2412.05032
See Also
mboot estimate.tau
Examples
data <- runif(1000)
estimate.max <- function(data, indices) {return(max(data[indices]))}
tau <- function(n){n} # convergence rate (usually sqrt(n), but n for max)
boot.out <- mboot(data, estimate.max, R = 1000, m = 2*sqrt(NROW(data)), replace = FALSE)
cis <- mboot.ci(boot.out, 0.95, tau, c("all"))
ci.basic <- cis$basic
print(ci.basic)