Abstract

Multivariate isotonic regression theory plays an important role in the field of testing statistical hypotheses under order restriction for several vector valued parameters and this problem may arise in several situations. Sasabuchi et al. derived a likelihood ratio type test for homogeneity of order restricted mean vectors under a multivariate normality assumption with unknown and common covariance matrices; however, its null distribution depends on the unknown covariance matrix. In order to overcome this difficulty, in the present paper we propose a test that conditions on the sufficient statistic for the covariance matrix. We remove the dependence of the null distribution of test statistic proposed by Sasabuchi et al. on the unknown value of covariance matrix and present a condition on a sufficient statistic for covariance matrix under the null hypothesis. A method based on Markov Chain Monte Carlo sampling is used to calculate the $p-$value of the test. We evaluate the operating characteristics of the proposed test through simulation studies. Our extensive simulation studies demonstrate that the power of this new test is generally higher than the test proposed by Sasabuchi et al. and also by Sasabuchi. A real data example is presented.

摘要

多元等渗回归理论在检验统计假设领域中的几个向量值参数的顺序限制下发挥着重要作用，这个问题可能会出现在几种情况下。Sasabuchi 等人。在具有未知和常见协方差矩阵的多元正态假设下，推导出阶数受限均值向量的同质性似然比类型检验；然而，它的零分布取决于未知的协方差矩阵。为了克服这个困难，在本论文中，我们提出了一个以协方差矩阵的充分统计为条件的检验。我们消除了 Sasabuchi 等人提出的检验统计量的零分布的依赖性。关于协方差矩阵的未知值，并提出在原假设下协方差矩阵的充分统计量的条件。一种基于马尔可夫链蒙特卡洛抽样的方法用于计算$p-$测试的价值。我们通过模拟研究评估了拟议测试的操作特性。我们广泛的模拟研究表明，这种新测试的功效通常高于 Sasabuchi 等人提出的测试。还有笹渊。提供了一个真实的数据示例。