unif.2017YMq | R Documentation |
Given a multivariate sample X, it tests
H_0 : Σ_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.
unif.2017YMq(X, lower = rep(0, ncol(X)), upper = rep(1, ncol(X)))
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. |
a (list) object of S3
class htest
containing:
a test statistic.
p-value under H_0.
alternative hypothesis.
name of the test.
name(s) of provided sample data.
yang_multivariate_2017SHT
## 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=""))
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