Iboot (version 0.1-1)

Iboot-package: Iboot: iterated bootstrap tests and confidence sets

Description

The package provides a computationally efficient and general algorithm to obtain iterated bootstrap tests and confidence sets based on the unstudentised version of the Rao statistic for a $p$-dimensional parameter. The outer and inner level of resampling required to obtain respectively the simple and the re-calibrated bootstrap critical values (at the null hypothesys) are performed in a weighted fashion. The particular choice of the resampling weights allows to obtain accurate re-calibrated critical values with one level of bootstrap iteration only (Lee and Young, 2003).

The algorithm is particularly efficient as it combines a deterministic stopping rule (Nankervis, 2005) and a computationally convenient statistic to bootstrap on (Lunardon, 2013).

Details

Function Iboot is merely an R wrapper to call a set of foreign functions all written in C language so that computational efficiency is increased. Some C routines are borrowed from R sources: numerical optimisation and sorting relies on lbfgsb and revsort located in "/src/main/optim.c" and "/src/main/sort.c", respectively. The function ProbSampleReplace for sampling with unequal probabilities has been slightly modified to cut down the number of unnecessary operations for bootstrap resamplings.

References

Lee, S., Young, A. (2003). Prepivoting by weighted bootstrap iteration. Biometrika, 90, 393--410.

Lunardon, N. (2013). Prepivoting composite score statistics by weighted bootstrap iteration. E-print: arXiv/1301.7026.

Nankervis, J. (2005). Computational algorithms for double bootstrap confidence intervals. Computational statistics & data analysis, 45, 461--475.

See Also

one.boot, boot, stats.

Examples

####Example 1: mean of a normal with known scale
n <- 20
mu <- 1

set.seed(1)
##contributions obtained from the score function
gr <- rnorm(n, mu) - mu

OBJ.Ib <- Iboot(gradient=gr, B=500, M=500, kB=0.01, alpha=c(0.1, 0.05, 0.01), seed=1)

##critical values for testing H0: mu=1, H1: mu!=1
OBJ.Ib
summary(OBJ.Ib)

####Example 2: variance of a normal with known location
n <- 20
mu <- 1
sig2 <- 1

set.seed(1)
##contributions obtained from the score function
gr <- ( rnorm(n, mu, sqrt(sig2)) - mu )^2/sig2 - 1

OBJ.Ib <- Iboot(gradient=gr, B=500, M=500, kB=0.01, alpha=c(0.1, 0.05, 0.01), seed=3)

##critical values for testing H0: sig2=1, H1: sig2!=1
OBJ.Ib
summary(OBJ.Ib)