Existing methods for dimension reduction in regression estimate a subspace in the primal predictor-based space, and then obtain the set of reduced predictors by projecting the original predictor vector onto this subspace. We propose a principled method for estimating a sufficient reduction in the dual sample-based space, on the basis of a supervised inverse regression model. Reduction is done without the need to estimate the subspace. Our method extends the duality between principal component analysis and principal coordinate analysis. We study the asymptotic behavior of the proposed method, and demonstrate that it is robust to model misspecification. We present simulation results to support the theoretical conclusion, and illustrate the application of the method in real

中文翻译：

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关于监督归约及其对偶

回归中降维的现有方法在基于原始预测器的空间中估计一个子空间，然后通过将原始预测器向量投影到该子空间上来获得减少的预测器集合。我们提出了一种基于监督逆回归模型来估计基于双样本空间的充分减少的原理方法。无需估计子空间即可完成归约。我们的方法扩展了主成分分析和主坐标分析之间的对偶性。我们研究了所提出方法的渐近行为，并证明了它对模型错误指定的鲁棒性。我们提供了仿真结果来支持理论结论，并说明该方法在实际中的应用