异方差情形下多元方差分析中新的广义p值

New Generalized p-Values for MANOVA under Unequal Covariances

对于带有不相等协方差矩阵的多元方差分析问题,一类新的广义检验变量被定义去检验k个多元正态均值向量的相等性假设.基于该广义检验变量的广义p值是充分统计量的函数,当k=2时,即对于多元Behrens-Fisher问题,该新的广义检验变量和Gamage等提供的变量等价.数值结果表明,所得的广义p值检验能够保证第一类错误概率不超过名义水平,且其优于经典的似然比检验和Gamage等提供的检验.

For MANOVA problem under unequal covariance matrices, a new class of generalized test variable was defined to test the equality of the mean vectors of k multivariate normal popula- tions based on the concept of generalized p-values. The generalized p-values based on these gen- eralized test variables were functions of sufficient statistics. It was shown that for the case k= 2, i.e. the multivariate Behrens-Fisher problem, the new generalized test variables were equivalent to that proposed by Gamage et al. Numerical results showed that our generalized p-values test for comparing the equality of several mean vectors had a type I error probability not exceeding the nominal level and it was better than the classical likelihood ratio test and the procedure given by Gamage et al.