【摘要】 设Xj1,Xj2,…,XjNj(j=1,2,…,q)为从q个p维实正态总体Npθj,12Σj抽取的一个随机子样,原假设为H:Σ1=Σ2=…=Σq=σ2Ip(其中σ2>0未知,Ip为P阶单位矩阵).文章证明了修改似然比检验的势函数仅与Σj(j=1,2,…,q)的特征根有关,并给出了其势函数的单调性结论.更多还原

【Abstract】 Let Xj1,Xj2,…,XjNj(j=1,2,…,q)be random samples of size Nj from q normal populations with mean μj and positive definite covariance matrix 12Σj and null hypothesis be H:Σ1=Σ2=…=Σq=σ2Ip,where σ2>0 is unknown and Ip is unit matrix.In this paper,we prove that the power function of the modified likelihood ratio test depends only on the characteristic roots of Σj.The monotonicity of this power function is given.更多还原