In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we propose a new method of local search to estimate the structural dimensions. Simulations and real data analysis support the efficiency and effectiveness of the proposed method.

中文翻译：

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通过距离协方差对矩阵值预测变量进行足够的维数折叠

在现代数据中，当预测变量具有矩阵/数组值时，由于结构复杂，建立合理的模型要困难得多。但是，尺寸折叠可以减小预测变量的尺寸，同时又保持其结构，这对于帮助构建有用的模型至关重要。在本文中，我们开发了一种使用距离协方差进行回归的新的足够维折叠方法。该方法无需对预测变量进行严格假设即可有效工作。它是无模型且非参数的，但既不需要平滑技术也不需要选择调整参数。而且，它适用于单变量和多变量响应情况。另外，我们提出了一种新的局部搜索方法来估计结构尺寸。仿真和真实数据分析证明了该方法的有效性和有效性。