论文标题
针对高维拆分图设计具有不同维度的高维拆分设计的推断
Inference for high-dimensional split-plot designs with different dimensions between groups
论文作者
论文摘要
在多个组的重复测量设计中，主要目的是比较各个方面的不同组。由于几个原因，测量数量以及观察向量的维度可以取决于组，从而使现有方法的使用不可能。我们开发了一种方法，该方法不仅可以用于可能增加的组$ a $，还可以用于群体底部的尺寸$ d_i $，该尺寸可以允许使用无限。这是一个独特的高维渐近框架，其多样性给人留下了深刻的印象，并且在样本量和维度之间的关系中没有通常的条件。它尤其包括在某些组中具有固定尺寸的设置以及其他尺寸增加的设置，而其他尺寸可以看作是半高维的。为了找到适当的统计测试，开发了新的和创新的估计器，可以在$ a，d_i $和$ n_i $的这些不同设置下使用，而无需任何调整。我们研究了基于二次形式的测试统计数据的渐近分布，并开发了渐近的正确测试。最后，进行了广泛的模拟研究，以研究单个组维度的作用。
In repeated Measure Designs with multiple groups, the primary purpose is to compare different groups in various aspects. For several reasons, the number of measurements and therefore the dimension of the observation vectors can depend on the group, making the usage of existing approaches impossible. We develop an approach which can be used not only for a possibly increasing number of groups $a$, but also for group-depending dimension $d_i$, which is allowed to go to infinity. This is a unique high-dimensional asymptotic framework impressing through its variety and do without usual conditions on the relation between sample size and dimension. It especially includes settings with fixed dimensions in some groups and increasing dimensions in other ones, which can be seen as semi-high-dimensional. To find a appropriate statistic test new and innovative estimators are developed, which can be used under these diverse settings on $a,d_i$ and $n_i$ without any adjustments. We investigated the asymptotic distribution of a quadratic-form-based test statistic and developed an asymptotic correct test. Finally, an extensive simulation study is conducted to investigate the role of the single group's dimension.
