标题： 分类的充分维度降低 显示英文标题

标题： Sufficient Dimension Reduction for Classification

摘要： 我们提出了一种新的充分维度缩减方法，专门针对高维分类设计。 这种新方法被称为最大均值方差（MMV），受到Cui、Li和Zhong（2015）首次提出的均值方差指数的启发，该指数衡量多类分类随机变量与连续随机变量之间的依赖关系。 我们的方法对预测变量提出了合理适度的限制，并且无需估计链接函数即可保持模型无关的优势。 在固定和发散维度（p）情况下，MMV估计量的一致性在常规条件下得到建立，响应类别数量也可以随着样本量n的增加而发散。当预测向量的维度固定时，我们还构建了估计量的渐近正态性。 此外，当n < p时，我们的方法表现良好。通过模拟研究和实际数据分析，展示了所提方法的显著分类效率提升。 显示英文摘要

摘要： We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and Zhong (2015), which measures the dependence between a categorical random variable with multiple classes and a continuous random variable. Our method requires reasonably mild restrictions on the predicting variables and keeps the model-free advantage without the need to estimate the link function. The consistency of the MMV estimator is established under regularity conditions for both fixed and diverging dimension (p) cases and the number of the response classes can also be allowed to diverge with the sample size n. We also construct the asymptotic normality for the estimator when the dimension of the predicting vector is fixed. Furthermore, our method works pretty well when n < p. The surprising classification efficiency gain of the proposed method is demonstrated by simulation studies and real data analysis.