oceCens (version 0.1.2)

percci: Percentile Bootstrap Two-sided Confidence Intervals and p-values

Description

Input vector of bootstrap replicates and get either the two-sided percentile confidence interval or the compatible two-sided p-value.

Usage

percci(Ti, conf.level = 0.95)
percpval(Ti, theta0 = 0)

Value

percci returns only a two-sided confidence interval and

percpval returns only a two-sided p-value.

Arguments

Ti

A numeric vector of bootstrap replicates of an estimate.

conf.level

Confidence level.

theta0

Null hypothesis value of estimand.

Functions

• percpval(): Bootstrap percentile p-values

Details

Simple functions, where percci gives two-sided confidence intevals and percpval gives two-sided p-values.

We get a two-sided p-value by inverting the percentile Bootstrap confidence interval. This is not straightforward if there are not enough bootstrap samples and/or if the minimum and maximum of the replicates do not cover the null value. If there are B bootstrap resamples, then the interval from the minimum to the maximum has confidence level =1- 2/(B+1). We can see this because the percentile interval (see Efron and Tibshirani, 1993, p. 160 bottom) is T[k], T[B+1-k] where k=floor( (B+1)*(1-conf.level)/2), where T is an ordered vector of B test statistics calculated from B bootstrap replicates (T=Ti[order(Ti)]). Therefore, if conf.level > 1 - 2/(B+1) then we cannot get a percentile interval, so if the min and max of T do not surround theta0, then a two-sided p-value can be stated to be p<= 2/(B+1). If the p-value is 2/(B+1), then it is the lowest possible for that B, and increasing B may produce a lower p-value.

References

Efron, B and Tibshirani, RJ (1993) An Introduction to the Bootstrap. Chapman and Hall.

Examples

# \donttest{
  set.seed(123)
  y<- rnorm(100)+0.1
  nB<- 1e5
  Tstat<- rep(NA,nB)
  for (i in 1:nB){
    Tstat[i]<-mean( sample(y,replace=TRUE) )
   }
   # two-sided bootstrap percentile p-value
   # that mean is different from 0
   percpval(Tstat,theta0=0)
   # 95% percentile interval
   percci(Tstat)
   # compare to t-test
   t.test(y)

   # to show that the functions are close to compatiable
   # set confidence level to 1-pvalue
   pval<-percpval(Tstat,theta0=0)
   confLevel<- 1-pval
   pval
   # then lower limit should be close to 0
   percci(Tstat, conf.level=confLevel)
  # }