unif.2017YMq {SHT}

Multivariate Test of Uniformity based on Normal Quantiles by Yang and Modarres (2017)

Description

Given a multivariate sample X, it tests

H_0 : \Sigma_x = \textrm{ uniform on } \otimes_{i=1}^p [a_i,b_i] \quad vs\quad H_1 : \textrm{ not } H_0

using the procedure by Yang and Modarres (2017). Originally, it tests the goodness of fit on the unit hypercube [0,1]^p and modified for arbitrary rectangular domain. Since this method depends on quantile information, every observation should strictly reside within the boundary so that it becomes valid after transformation.

Usage

unif.2017YMq(X, lower = rep(0, ncol(X)), upper = rep(1, ncol(X)))

Arguments

X

an (n\times p) data matrix where each row is an observation.

lower

length-p vector of lower bounds of the test domain.

upper

length-p vector of upper bounds of the test domain.

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

Yang M, Modarres R (2017). “Multivariate tests of uniformity.” Statistical Papers, 58(3), 627–639. ISSN 0932-5026, 1613-9798.

Examples

## CRAN-purpose small example
smallX = matrix(runif(10*3),ncol=3)
unif.2017YMq(smallX) # run the test


## empirical Type 1 error 
niter   = 1234
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  X = matrix(runif(50*5), ncol=25)
  counter[i] = ifelse(unif.2017YMq(X)$p.value < 0.05, 1, 0)
}

## print the result
cat(paste("\n* Example for 'unif.2017YMq'\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=""))