Silvapulle M J
School of Agriculture, La Trobe University, Bundoora, Australia.
Biometrics. 1994 Sep;50(3):853-8.
One-sided hypotheses arise naturally in many situations. When testing against such hypotheses, it is desirable to take the available one-sided information into account, rather than simply applying a two-sided test. What we expect to gain by applying a one-sided test instead of a two-sided test is an increase in the power of the test. We consider various tests of one-sided hypotheses in a class of models that includes generalized linear and Cox regression models. The tests are likelihood ratio, Wald, score, generalized distance, and a Pearson chi-square. It is shown that these test statistics are asymptomatically equivalent in terms of local power; this is a generalization of the well-known corresponding result for two-sided alternatives. Two examples are also discussed. They are on (1) testing for interaction in binomial response models, and (2) comparison of treatments with ordinal categorical responses.
单侧假设在许多情况下自然出现。在针对此类假设进行检验时，考虑可用的单侧信息而非简单应用双侧检验是很有必要的。相较于双侧检验，应用单侧检验我们期望获得的是检验功效的提升。我们在一类包括广义线性模型和Cox回归模型的模型中考虑各种单侧假设检验。这些检验包括似然比检验、 Wald检验、得分检验、广义距离检验以及Pearson卡方检验。结果表明，就局部功效而言，这些检验统计量是渐近等价的；这是关于双侧备择假设的著名相应结果的推广。还讨论了两个例子。它们分别是(1) 二项响应模型中的交互作用检验，以及(2) 有序分类响应的治疗比较。
