abcnonHtest {asht}

Nonparametric ABC (Approximate Bootstrap Confidence) intervals.

Description

A hypothesis testing function using the nonparametric ABC intervals.

Usage

abcnonHtest(x, tt, nullValue = NULL, conf.level = 0.95, 
   alternative = c("two.sided", "less", "greater"), epsilon = 0.001, minp = 0.001)

Arguments

x

the data. Must be either a vector, or a matrix whose rows are the observations

tt

function defining the parameter in the resampling form tt(p,x), where p is the vector of proportions and x is the data

nullValue

null value of the parameter for the two-sided hypothesis test, or boundary of null parameter space for one-sided ones

conf.level

confidence level for interval

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

epsilon

optional argument specifying step size for finite difference calculations

minp

minimum p-value (used in uniroot search to give a bound, toe two.sided alternatives actual minimum is 2*minp)

Details

Calculates the nonparametric ABC confidence interval of DiCiccio and Efron (1992). See also Efron and Tibshirani (1993).

The p-values are calculated by solving for confidence limit that just touches the nullValue. If it is outside of the range (minp, 1-minp) for one-sided p-values, then it is set to minp. If it is outside the range (2*minp, 1- 2*minp) for two-sided p-values, then it is set to 2*minp.

Value

A value of class "htest" containing the following components:

p.value

p-value for test defined by alternative and nullValue

estimate

estimate of the parameter, calculated using x and the tt function

conf.int

confidence interval for the parameter associated with tt

null.value

the nullValue (or null boundary) for the hypothesis test

alternative

a character string describing the alternative hypothesis

method

a character string describing the kind of test

data.name

a character string giving the name of the data and the function

Author(s)

the function is modification of abcnon in the bootstrap R package, originally written by Rob Tibshirani, modifications by M.P. Fay

References

DiCiccio, T and Efron, B (1992). More accurate confidence intervals in exponential families. Biometrika 79: 231-245.

Efron, B and Tibshirani, RJ (1993). An introduction to the bootstrap. Chapman and Hall: New York.

See Also

See also abcnon.

Examples

# compute abc intervals for the mean
x <- c(2,4,12,4,6,3,5,7,6)
theta <- function(p,x) {sum(p*x)/sum(p)}
## smallest p-value is 2*minp for two-sided alternatives
abcnonHtest(x, theta, nullValue=0)  
## test null at 95% confidence limit is like just barely
## rejecting at the two-sided 5% level, so p-value is 0.05
abcnonHtest(x, theta, nullValue=4.072772)  
# compute abc intervals for the correlation
set.seed(1)
x <- matrix(rnorm(20),ncol=2)
theta <- function(p, x)
{
    x1m <- sum(p * x[, 1])/sum(p)
    x2m <- sum(p * x[, 2])/sum(p)
    num <- sum(p * (x[, 1] - x1m) * (x[, 2] - x2m))
    den <- sqrt(sum(p * (x[, 1] - x1m)^2) *
              sum(p * (x[, 2] - x2m)^2))
    return(num/den)
}
abcnonHtest(x, theta) 
## compare with 
## Not run: 
library(bootstrap)
abcnon(x, theta, alpha=c(.025,.975))$limits[,"abc"]
## End(Not run)