On an F-type statistic for testing one-sided hypotheses and computation of chi-bar-squared weights

A natural generalization of the well-known F-statistic is introduced for testing one-sided hypotheses. The exact finite sample null distribution of this statistic is shown to be a weighted sum of F-distributions. This resembles the large sample null distribution of the likelihood ratio statistic, a chi-bar squared distribution, which is a weighted sum of [chi]2 distributions. It turns out that the weights in these two distributions are identical; this is an important feature because we can use essentially the same computer programs for computing the p-values for the F- and the likelihood ratio statistics. A general stimulation procedure for computing the chi-bar-squared weights when the linear inequalities in the alternative hypothesis are not independent is introduced