线性模型中假设是凸锥时似然比统计量的零分布

NULL DISTRIBUTION OF LIKELIHOOD RATIO STATISTIC FOR AND AGAINST CONVEX CONES IN THE LINEAR MODEL

对于有正态误差和已知协方差阵的线性模型，讨论了参数域是凸锥的假设检验问题．在考察了似然比统计量的性质后，表明了只要似然比统计量是观察值的凸函数，则似然比统计量的零分布是Ｘ２－分布的混合，而此前的结果是仅当零假设或备择假设形成线性空间时才可用．

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.