复生长曲线模型中参数的无偏似然比检验准则

摘要

讨论了复生长曲线模型中尺度参数∑和位置参数ξ的检验问题．设原假设为①H1：∑=Ip（Ip为P阶单位阵）；②H2：∑=Ip且ξ：0（0为q×m阶零矩阵）；③H3：∑=σ2Ip（σ2〉0且未知）．证明了当A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.