One-sample Test for Mean Vector by Dempster (1958, 1960)

Given a multivariate sample $X$ and hypothesized mean $\mu_0$ , it tests $H_0 : \mu_x = \mu_0\quad vs\quad H_1 : \mu_x \neq \mu_0$ using the procedure by Dempster (1958, 1960).

mean1.1958Dempster(X, mu0 = rep(0, ncol(X)))

Arguments

X: an $(n\times p)$ data matrix where each row is an observation.
mu0: a length- $p$ mean vector of interest.

Value

a (list) object of S3 class htest containing:

statistic: a test statistic.
p.value: $p$ -value under $H_0$ .
alternative: alternative hypothesis.
method: name of the test.
data.name: name(s) of provided sample data.

References

Dempster AP (1958). “A High Dimensional Two Sample Significance Test.” The Annals of Mathematical Statistics, 29(4), 995--1010. ISSN 0003-4851.

Dempster AP (1960). “A Significance Test for the Separation of Two Highly Multivariate Small Samples.” Biometrics, 16(1), 41. ISSN 0006341X.

Examples

## CRAN-purpose small example
smallX = matrix(rnorm(10*3),ncol=3)
mean1.1958Dempster(smallX) # run the test
#> 
#> 	One-sample Test for Mean Vector by Dempster (1958).
#> 
#> data:  smallX
#> statistic = 0.69274, p-value = 0.5642
#> alternative hypothesis: true mean is different from mu0.
#> 

# \donttest{
## empirical Type 1 error 
niter   = 1000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  X = matrix(rnorm(50*5), ncol=50)
  counter[i] = ifelse(mean1.1958Dempster(X)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'mean1.1958Dempster'\n","*\n",
"* number of rejections   : ", sum(counter),"\n",
"* total number of trials : ", niter,"\n",
"* empirical Type 1 error : ",round(sum(counter/niter),5),"\n",sep=""))
#> 
#> * Example for 'mean1.1958Dempster'
#> *
#> * number of rejections   : 71
#> * total number of trials : 1000
#> * empirical Type 1 error : 0.071
# }