ABSTRACT In this article, we propose a new method for sufficient dimension reduction when both response and predictor are vectors. The new method, using distance covariance, keeps the model-free advantage, and can fully recover the central subspace even when many predictors are discrete. We then extend this method to the dual central subspace, including a special case of canonical correlation analysis. We illustrated estimators through extensive simulations and real datasets, and compared to some existing methods, showing that our estimators are competitive and robust.

中文翻译：

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通过多变量响应的距离协方差进行充分的降维

摘要 在本文中，我们提出了一种新方法，当响应和预测变量都是向量时，可以进行充分的降维。使用距离协方差的新方法保持了无模型优势，即使在许多预测变量是离散的情况下也可以完全恢复中心子空间。然后我们将此方法扩展到对偶中心子空间，包括典型相关分析的特殊情况。我们通过广泛的模拟和真实数据集说明了估算器，并与一些现有方法进行了比较，表明我们的估算器具有竞争力和稳健性。