Statistical inference for parallelism hypothesis in growth curve model
Statistical inference for parallelism hypothesis in growth curve model
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DOI：
10.55937/sut/1266408621
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发表时间：
2009-06
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通讯作者：
Y. Fujikoshi
中科院分区：
文献类型：
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作者：
Y. Fujikoshi
设y = （y1，…）， yp) '是一个p维随机向量，可测量从k个p维正常总体中抽取的每个个体Πi: Np（-i，Σ）， i = 1，…本文考虑具有如下平均结构的生长曲线模型：-i = X ' i, i = 1，…。， k，其中X是给定秩为q的矩阵的pxq， i是未知的参数向量。首先，我们推导了平行假设H1的LR检验：X ' i−X ' k = γi1p, i = 1，…。， k−1，其中γi是未知参数，1p是包含所有元素1的p维向量。然后我们得到，= （γ1，…）的最大似然。， γk−1)′及其分布，并提出了，的线性组合的同时置信区间。AMS 2000数学学科分类。62H12, 62E20。
Let y = (y1, ..., yp) ′ be a p-dimensional random vector measurable on the individuals drawn from each of k p-dimensional normal populations Πi : Np(—i,Σ), i = 1, . . . , k. In this paper we consider the growth curve model which has a mean structure as follows: —i = X„i, i = 1, . . . , k, where X is a p× q given matrix with rank q and „i’s are unknown parameter vectors. First we derive an LR test for a parallelism hypothesis H1 : X„i−X„k = γi1p, i = 1, . . . , k − 1, where γi’s are unknown parameters, and 1p is the p-dimensional vector with all the elements 1. Next we obtain the MLE of ‚ = (γ1, . . . , γk−1)′ and its distribution, and propose a simultaneous confidence interval for linear combinations of ‚. AMS 2000 Mathematics Subject Classification. 62H12, 62E20.