Asymptotic properties of likelihood ratio statistics on non-inferiority hypothesis testing

我们有以下两个研究结果：1。在基本分布呈指数分布且数据服从I型审查的生存模型中，讨论了一些治疗之间的非劣效检验问题。在两样本和k样本情况下，推导了似然比统计量的渐近分布。提出了一种基于似然比统计的非劣效性检验假设的检验方法。基于似然比统计，讨论了两种治疗间的非劣效检验问题。设两种处理的基础分布为正态分布，分别为平均值θ和平均值μ，共有未知方差。我们考虑以下一般假设，包括非劣性假设：H_0:θ≧h(μ) vs . H_1:θ<h(μ)，其中h（μ）是任意连续严格递增函数。在这种情况下，得到了对数似然比统计量在假设边界真值下的渐近分布。当真值为任意可微点时，其渐近分布为1/2+(1/2)x^2_1，与函数h（μ）无关，其中x^2_1为一自由度的卡方随机变量。另一方面，如果真点是函数h（,μ）的任何不可微点，则其渐近分布以依赖函数h（μ）的左右微分系数的形式表示。

We have the following two research results.1.The non-inferiority testing problem between some treatments is discussed in survival model where the underlying distribution is exponential and data are subject to type I censoring. The asymptotic distribution of the likelihood ratio statistic is derived in two-sample and k-sample cases. One testing procedure for the non-inferiority testing hypotheses is proposed based on the likelihood ratio statistic.2.The non-inferiority testing problem between two treatments is discussed based on the likelihood ratio statistic. Let the underlying distribution for the two treatments be normally distributed with mean θ and μ, respectively, and common unknown variance. We consider the following general hypotheses including the non-inferiority hypotheses : H_0:θ≧h(μ) v.s. H_1:θ<h(μ), where h(μ)is any continuous and strictly increasing function. In this situation, the asymptotic distribution of the log-likelihood ratio statistic is obtained under the true value on the boundary of the hypotheses. When the true value is any differentiable point, the asymptotic distribution becomes 1/2+(1/2)x^2_1 irrespective to the function h(μ), where x^2_1 is the chi-squared random variable with one degree of freedom. On the other hand, if the true point is any non-differentiable point for the function h(,μ), the asymptotic distribution is expressed in the form depending on right and left differential coefficients of the function h(μ).