moonboot (version 2.0.1)

mboot.ci: 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 the 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", ...)

Value

A list of confidence intervals for the given types.

Arguments

boot.out

The simulated bootstrap distribution from the mboot call.

conf

The confidence level.

tau

Function that returns the scaling factor tau in dependence of n. If NULL, estimate.tau is used to estimate tau.

types

The types of confidence intervals to be calculated. The value can be 'all' for all types, or a subset of c("basic", "norm", "sherman").

...

When tau is omitted, the additional parameters are passed to statistic during estimation of tau.

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 the confidence intervals are supported through the parameter type:

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.

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, tools:::Rd_expr_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 F. (2025) moonboot: An R Package Implementing m-out-of-n Bootstrap Methods tools:::Rd_expr_doi("10.32614/RJ-2025-031")

See Also

mboot estimate.tau

Examples

# statistic for univariate data: maximum
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, conf=0.95, tau=tau, types=c("basic","norm"))
print(cis$basic)

# statistic for multivariate data: correlation
data <- data.frame(x = runif(1000))
data$y <- data$x + runif(1000)
estimate.cor <- function(data, indices) {return(cor(data$x[indices],data$y[indices]))}
boot.out <- mboot(data, estimate.cor, R = 1000, m = 2*sqrt(NROW(data)), replace = FALSE)
cis <- mboot.ci(boot.out, conf=0.95, tau=sqrt, types=c("basic","norm"))
print(cis$basic)