STATISTICAL INFERENCE BASED ON M-STATISTICS IN TWO-WAY MANOVA
STATISTICAL INFERENCE BASED ON M-STATISTICS IN TWO-WAY MANOVA
复制标题
双向方差分析中基于 M 统计量的统计推断
DOI：
10.11329/jjss1970.23.33
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
T. Shiraishi
中科院分区：
文献类型：
--
作者：
T. Shiraishi
考虑了具有交互作用的双向布局中的多响应·@实验，每个单元格具有相等数量的观测。基于M-统计量，给出了模型中交互作用和主效应的检验、估计和置信域的统计方法。当胞元尺寸趋于无穷大时，研究了它们的程序的大样本性质。M-过程的通常假设，即底层分布是对角对称的是不需要的。对于单变量的情况下，它被发现，所提出的程序相对于经典的程序的渐近相对效率（ARE的）同意与Huber的单样本M-估计相对于样本均值的经典ARE-结果。通过模拟研究，考察了M-检验的显著性点的x2-近似的优良性，并证明了M-估计对污染分布的稳健性。此外，还简要讨论了无交互作用双向MANOVA的M-过程。
Multiresponse•@ experiments in two-way layouts with interaction, having equal number of observations per cell, are considered. Statistical procedures of the test, estimation and confidence region, based on M-statistics, for interactions and main effects in the models are proposed. Large sample properties of their procedures as the cell size tends to infinity are investigated. The usual assumption of M-procedures that the underlying distribution is diagonally symmetric is not needed. For the uni variate case, it is found that the asymptotic relative efficiencies(A RE's) of the proposed procedures relative to classical procedures agree with the classical ARE-results of Huber's one sample M-estimator relative to the sample mean. By simulation studies, the goodness of the x2-approximate for the significance points of the M-tests is in vestigated, and it can be seen that the M-estimators are robust with respect to the contaminated distribution. Furthermore M-procedures for two-way MANOVA with out interaction are discussed briefly.