Li Changcheng, Li Runze
Department of Statistics, Pennsylvania State University at University Park.
J Am Stat Assoc. 2022;117(540):1738-1750. doi: 10.1080/01621459.2021.1884561. Epub 2021 Apr 27.
In this paper, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this paper. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example.
在本文中，我们针对具有高维响应的线性模型中回归系数矩阵的线性假设提出了一种新的投影检验。我们系统地研究了所提出检验的理论性质。我们首先为任何给定的投影维度推导最优投影矩阵以实现最佳功效，并给出投影矩阵最优维度的一个上界。我们进一步深入探讨了如何构建最优投影矩阵。单样本和两样本均值问题可以被表述为本文所研究的线性假设的特殊情况。我们从理论和实证两方面证明，对于单样本和两样本均值问题，所提出的检验比现有检验表现更优。我们进行蒙特卡罗模拟以检验有限样本性能，并通过一个实际数据例子来说明所提出的检验。
