复生长曲线模型中参数的无偏似然比检验准则

On the unbiasedness of some likelihood ratio test criteriain a complex grown curve model

讨论了复生长曲线模型中尺度参数Σ和位置参数ξ的检验问题.设原假设为①H1∶Σ=Ip(Ip为p阶单位阵);②H2∶Σ=Ip且ξ=0(0为q×m阶零矩阵);③H3∶Σ=σ2Ip(σ2>0且未知).证明了当Λ为分块对角矩阵时,相应于备择假设Ai≠Hi(i=1,2,3)检验原假设Hi的似然比检验是无偏的.

The problems on hypothetical testing of scale and location parameter in a complex growth curve model are considered in this paper. Suppose the null hypotheses are as follows：①H1：∑=Ip（Ip is an identity matrix of order p）;②H2：∑=Ip andξ：0（0 is a zero matrix of order q × m）;③H3：∑=σ2Ip（σ2 is unknown positive number）. It is derived that the likelihood tests of the null hypotheses Hi against above alternative hypotheses Ai≠Hi （ i = 1,2,3 ） are unbiased when ∑ is the form of block diagonal matrix in Section 2.