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 |

`mu0` |
a length- |

`Sigma0` |
a |

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.

## 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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