bootCI: Pointwise confidence intervals by bootstrap

Description

Pointwise quantiles and survival probabilities confidence intervals using bootstrap.

Usage

bootCI(X, weights = rep(1, length(X)), probs = 1:(length(X) -
  1)/length(X), xgrid = sort(X), B = 100, alpha = 0.05,
  type = "quantile", CritVal = 10, initprop = 1/10, gridlen = 100,
  r1 = 1/4, r2 = 1/20, plot = F)

Value

LowBound: the lower bound of the bootstrap (1-\(alpha\))-confidence interval.
UppBound: the upper bound of the bootstrap (1-\(alpha\))-confidence interval of level.

Arguments

X: a numeric vector of data values.
weights: a numeric vector of weights.
probs: used if type = "quantile", a numeric vector of probabilities with values in \([0,1]\).
xgrid: used if type = "survival", a numeric vector with values in the domain of X.
B: an integer giving the number of bootstrap iterations.
alpha: the type 1 error of the bootstrap (1-\(alpha\))-confidence interval.
type: type is either "quantile" or "survival".
CritVal: a critical value associated to the kernel function given by CriticalValue. The default value is 10 corresponding to the rectangular kernel.
gridlen, initprop, r1, r2: parameters used in the function hill.adapt (see hill.adapt).
plot: If TRUE, the bootstrap confidence interval is plotted.

Details

Generate B samples of \(X\) with replacement to estimate the quantiles of orders \(probs\) or the survival probability corresponding to \(xgrid\). Determine the bootstrap pointwise (1-\(alpha\))-confidence interval for the quantiles or the survival probabilities.

Examples

Run this code

X <- abs(rcauchy(400))
hh <- hill.adapt(X)
probs <- probgrid(0.1, 0.999999, length = 100)
B <- 200
if (FALSE)  #For computing time purpose
  bootCI(X, weights = rep(1, length(X)), probs = probs, B = B, plot = TRUE)
  xgrid <- sort(sample(X, 100))
  bootCI(X, weights = rep(1, length(X)), xgrid = xgrid, type = "survival", B = B, plot = TRUE)