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特别适用于生长曲线问题的广义多元方差分析模型AI 解读

The usual MANOVA (multivariate analysis of variance) model (see equation (1)) may be generalized (equation (3)) by allowing for the appending of a post-matrix in the expectation equation. As explained in §1, this generalized model (3) is applicable particularly to many kinds of growth curve problems, as well as to other problems. Section 2 is theoretical, and develops techniques of analysis under the generalized model. A numerical example involving growth curves is worked…

一类具有特定结构的矩阵的行列式、特征方程及其根的计算AI 解读

SUMMARY The variance–covariance matrices arising in the analysis of variance, response-surface fitting and order statistics have special patterns expediting and facilitating their algebraic manipulation. By appropriate triangulation and partitioning devices, the determinants of these matrices can be evaluated from general formulae. The characteristic equations, and sometimes their roots, can also be obtained in a direct single step.

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方差分析与多元分析若干非参数推广导论AI 解读

It is clear that a p-variate body of data arranged in a q-way classification will formally look llke a (p+q)-dimensional contingency table, but a distinction can be made between a ‘variate’ and a ‘way of classification’ in that along the direction of a ‘variate’ the marginal frequencies are supposed to be stochastic variates while along a ‘way of classification’ the marginal frequencies are supposed to be fixed. When, along certain directions, the marginals are fixed, an…