Assume that we have a random sample from an absolutely continuous distribution (univariate or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests symmetrically based on sample spacings. Asymptotic properties of these tests have been investigated under the simple null hypothesis and the sequence of local alternatives converging to the null hypothesis. The asymptotic properties of the proposed tests have also been studied under composite null hypothesis. It is observed that these tests have similar properties as the likelihood ratio test. For assessment of finite sample performance of the proposed tests, we have performed an extensive numerical study. The proposed tests can be used in some situations where likelihood ratio tests do not exist due to unboundedness of likelihood function.
翻译:假设我们有一个来自一个绝对连续分布(单变或多变)的随机样本,该样本具有已知功能形式和一些未知参数。在本文中,我们根据抽样间距研究了若干对称的参数测试。这些测试的无症状特性已经根据简单的无效假设和与无效假设相融合的当地替代品顺序进行了调查。还根据复合无效假设研究了拟议测试的无症状特性。据观察,这些测试的特性与可能性比率测试相似。为了评估拟议测试的有限样本性能,我们进行了广泛的数字研究。在可能比率测试因概率功能没有限制而不存在的情况下,可以使用拟议测试。