NULL DISTRIBUTION OF LIKELIHOOD RATIOSTATISTIC FOR AND AGAINST CONVEX CONES INTHE LINEAR MODEL
线性模型中假设是凸锥时似然比统计量的零分布

For the linear model with Gaussian errors and known covariance matrix, testingproblems are discussed where hypotheses form convex cones. After stating some properties ofthe likelihood ratio statistic, we show that the null distribution is a mixture of X2-distributionswhen the likelihood ratio statistic is a convex function of the observations. In contrast to this,the previous results are applicable only if the null or the alternative hypothesis forms a linearspace.