论文标题
ITDR：一组积分转换方法，用于估计回归中的SDR子空间
itdr: An R package of Integral Transformation Methods to Estimate the SDR Subspaces in Regression
论文作者
论文摘要
足够的尺寸降低（SDR）是回归模型的有效工具，提供了一种可行的方法来解决和分析回归问题的非线性性质。本文介绍了ITDR R软件包，这是一种全面且用户友好的工具，该工具基于基于积分转换方法的几个功能，用于估计SDR子空间。特别是，ITDR软件包包含了两种关键方法，即傅立叶方法（FM）和卷积方法（CM）。这些方法允许估计SDR子空间，即中央平均子空间（CMS）和中央子空间（CS），如果响应是单变量的，则可以估算中央平均值（CMS）和中央子空间（CS）。此外，ITDR软件包通过迭代的Hessian转换（IHT）方法促进了CMS的恢复，以实现单变量响应。此外，它通过采用各种傅立叶变换策略（例如倒数降低方法，使用傅立叶变换的最小差异方法以及傅里叶变换稀疏的逆回归方法，专门针对具有多元响应的病例设计的傅立叶变换）来实现CS的恢复。为了演示其功能，将ITDR软件包应用于五个不同的数据集。此外，该软件包是用于估计SDR子空间的积分转换方法的开创性实施，因此有望在SDR研究中取得重大进步。
Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and user-friendly tool that introduces several functions based on integral transformation methods for estimating SDR subspaces. In particular, the itdr package incorporates two key methods, namely the Fourier method (FM) and the convolution method (CM). These methods allow for estimating the SDR subspaces, namely the central mean subspace (CMS) and the central subspace (CS), in cases where the response is univariate. Furthermore, the itdr package facilitates the recovery of the CMS through the iterative Hessian transformation (IHT) method for univariate responses. Additionally, it enables the recovery of the CS by employing various Fourier transformation strategies, such as the inverse dimension reduction method, the minimum discrepancy approach using Fourier transformation, and the Fourier transform sparse inverse regression approach, specifically designed for cases with multivariate responses. To demonstrate its capabilities, the itdr package is applied to five different datasets. Furthermore, this package is the pioneering implementation of integral transformation methods for estimating SDR subspaces, thus promising significant advancements in SDR research.
