modernBoot (version 0.1.1)

studentized_ci: Studentized Bootstrap Confidence Interval for Quantiles

Description

Computes a studentized (t-based) bootstrap confidence interval for quantiles. More accurate than percentile intervals, especially for extreme quantiles.

Usage

studentized_ci(x, q = 0.5, R = 1000, Rinner = 200, conf = 0.95)

Value

A numeric vector of length 2 with names c("lower", "upper"):

lower

numeric, lower confidence limit for the q-th quantile

upper

numeric, upper confidence limit for the q-th quantile

Uses studentized bootstrap t-distribution to construct interval, providing better coverage probability than percentile method, especially for skewed distributions and extreme quantiles.

Arguments

x

numeric vector of data. May contain NAs which are removed. Minimum 2 observations required. Works well for skewed distributions and extreme quantiles where percentile bootstrap performs poorly.

q

numeric quantile level between 0 and 1 (default 0.5 for median). 0.25 = first quartile, 0.75 = third quartile, 0.95 = 95th percentile. Method particularly effective for extreme quantiles (q < 0.1 or q > 0.9).

R

integer number of outer bootstrap replicates (default 1000). This is primary bootstrap sample for t-distribution estimation. Recommended: 500-1000 for exploration, 2000+ for publication. Must be >= 1.

Rinner

integer number of inner bootstrap replicates for standard error estimation of each outer replicate (default 200). Larger values increase accuracy but also computation time (total iterations = R * Rinner). Recommended: 100-200. Must be >= 1.

conf

numeric confidence level between 0 and 1 (default 0.95). Standard: 0.95 or 0.99. Higher values give wider intervals.

Details

Studentized bootstrap uses the bootstrap t-distribution to construct intervals. This method often provides better coverage than percentile bootstrap, especially for skewed distributions or extreme quantiles.

Computation is intensive: O(R * Rinner) bootstrap samples are generated.

Examples

set.seed(42)
x <- rexp(30)  # Smaller sample: 30 instead of 50

# Fast example with reduced replications (< 5 sec) - UNWRAPPED
studentized_ci(x, q = 0.75, R = 100, Rinner = 20)

# \donttest{
# Larger, more accurate example (takes > 5 sec) - WRAPPED in \donttest
set.seed(42)
x <- rexp(50)
studentized_ci(x, q = 0.75, R = 1000, Rinner = 200)
# }