AI 中文总结
本研究提出一种基于逻辑回归的高维均值检验方法，通过逻辑Lasso筛选变量并经无惩罚重拟合推断，在多总体场景下具有高效性、渐近正确性和良好检验性能，适用于基因表达等实际高维数据。
AI 中文摘要
我们针对两个或多个高维总体的均值向量相等问题，提出了计算高效的检验方法。该方法的核心是均值相等与总体逻辑回归参数为零之间的等价关系，我们在不对各总体施加共同分布假设的独立观测场景下建立了这一等价关系。所提过程使用逻辑Lasso筛选信息变量，并在降维后进行无惩罚逻辑回归重拟合以开展推断，得到渐近正确的检验水平和一致性。对于指定的两样本高斯子模型及稀疏判别类别，该检验还达到了极小极大分离率。该框架可通过多类逻辑回归扩展至多总体场景。模拟结果显示，在不平衡设计和方差异质性条件下，与现有检验相比，所提方法具有准确的检验水平控制、强功效和良好的计算扩展性。对含超过22000个变量的基因表达数据的应用，进一步验证了所提过程的实际可扩展性。
英文摘要
We propose computationally efficient tests for equality of mean vectors of two or more high-dimensional populations. Central to our approach is an equivalence between equality of means and a zero population logistic regression parameter. We establish this equivalence for independently distributed observations without imposing common distributional assumptions across populations. Our procedure uses logistic Lasso to screen informative variables and an unpenalized logistic refit for inference in the reduced dimension, yielding asymptotically correct size and consistency. For a specified two-sample Gaussian submodel and sparse discriminative class, the test also attains the minimax separation rate. The framework extends to multiple populations through multi-class logistic regression. Simulations demonstrate accurate size control, strong power, and favorable computational scaling compared with existing tests under unbalanced designs and variance heterogeneity. Applications to gene-expression data with more than twenty-two thousand variables illustrate the practical scalability of the proposed procedures.
