生长曲线模型中参数的检验问题

The problem on testing expectation and covariance in growth curve model

讨论了生长曲线模型中关于原假设为H0:Λ=σ2I,μ=μ0的检验问题,并以2-分布为基础的级数形式给出了似然比检验统计量在以下两类与原假设相接近的备择假设下的渐近分布.K1:I-ηΛ-1=M2Ω,η-1/2(μ1-μ0)=M-1/2δ;K2:I-η-1Λ=M2Q,η-1/2(μ1-μ0)=M-1/2δ.

In the paper, the problem for tesing hypothesis H0：A=σ^2I,μ=μ0 is discussed in growth curve model. Asymptotic distributions of a certain function of likelihood ratio statistic have derived in a series of Chi-square distribution under two alternatives which are close to the null hypothesis as follows ： K1：I-ηA^-1=2/M Ω,η^（-1/2） （μ1-μ0）=M^（-1/2）δ;K2：I-η^-1 A=（2/M）Q,η^（-1/2） （μ1-μ0）=M^（-1/2）δ.