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

In Iboot: 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.

Author(s)

Nicola Lunardon <[e-mail]>.

Maintainer: Nicola Lunardon <[e-mail]>.

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)

Example output

Loaded Iboot 0.1-1


Observed value: 0.726 

Bootstrap quantile(s):
  90%   95%   99% 
2.758 3.975 6.322 

Re-calibrated bootstrap quantile(s):
93.4%   98% 99.8% 
3.445 5.382 8.350 

Algorithm ended succesfully.
Actual proportion of convex hull condition failures: 0 


Call: 
Iboot(gradient = gr, B = 500, M = 500, kB = 0.01, alpha = c(0.1, 
    0.05, 0.01), seed = 1)

Bootstrap distribution:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.122   0.484   1.026   1.401   9.572 

Observed value: 0.726 

Bootstrap quantile(s):
  90%   95%   99% 
2.758 3.975 6.322 

Re-calibrated bootstrap quantile(s):
93.4%   98% 99.8% 
3.445 5.382 8.350 

Algorithm ended succesfully.
Actual proportion of convex hull condition failures: 0 


Observed value: 0.5874 

Bootstrap quantile(s):
   90%    95%    99% 
 4.531  6.862 12.725 

Re-calibrated bootstrap quantile(s):
 93.6%  98.2%  99.8% 
 6.012 10.651 20.332 

Algorithm ended succesfully.
Actual proportion of convex hull condition failures: 0.006 


Call: 
Iboot(gradient = gr, B = 500, M = 500, kB = 0.01, alpha = c(0.1, 
    0.05, 0.01), seed = 3)

Bootstrap distribution:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  0.000   0.223   0.809   1.794   2.165  20.484 

Observed value: 0.5874 

Bootstrap quantile(s):
   90%    95%    99% 
 4.531  6.862 12.725 

Re-calibrated bootstrap quantile(s):
 93.6%  98.2%  99.8% 
 6.012 10.651 20.332 

Algorithm ended succesfully.
Actual proportion of convex hull condition failures: 0.006 

Iboot documentation built on May 2, 2019, 5:07 a.m.