sim1.LRT | R Documentation |
Given a multivariate sample X, hypothesized mean μ_0 and covariance Σ_0, it tests
H_0 : μ_x = μ_0 \textrm{ and } Σ_x = Σ_0 \quad vs\quad H_1 : \textrm{ not } H_0
using the standard likelihood-ratio test procedure.
sim1.LRT(X, mu0 = rep(0, ncol(X)), Sigma0 = diag(ncol(X)))
X |
an (n\times p) data matrix where each row is an observation. |
mu0 |
a length-p mean vector of interest. |
Sigma0 |
a (p\times p) given covariance matrix. |
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.
## CRAN-purpose small example smallX = matrix(rnorm(10*3),ncol=3) sim1.LRT(smallX) # run the test ## Not run: ## empirical Type 1 error niter = 1000 counter = rep(0,niter) # record p-values for (i in 1:niter){ X = matrix(rnorm(100*10), ncol=10) counter[i] = ifelse(sim1.LRT(X)$p.value < 0.05, 1, 0) print(paste("* iteration ",i,"/1000 complete...")) } ## print the result cat(paste("\n* Example for 'sim1.LRT'\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="")) ## End(Not run)
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