Linear Hypothesis Testing in Linear Models With High-Dimensional Responses
针对高维响应线性模型中的回归系数矩阵线性假设，提出一种新的投影检验方法，推导最优投影矩阵并给出理论性质，在单样本和两样本均值问题中优于现有方法。
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.