Fourier transform approach for inverse dimension reduction method
Fourier transform approach for inverse dimension reduction method
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DOI：
10.1080/10485252.2018.1515432
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发表时间：
2018-08
影响因子：
1.2
通讯作者：
Jiaying Weng;Xiangrong Yin
中科院分区：
文献类型：
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作者：
Jiaying Weng;Xiangrong Yin
摘要逆回归空间的估计在充分降维方面尤为重要。然而，它通常需要调优参数，例如切片方法中的切片数量或内核估计方法中的带宽选择。这样的要求不仅影响了有限样本下估计的精度，而且增加了多变量模型的难度。在本文中，我们使用傅里叶变换的方法来避免这样的困难，并结合多变量模型。我们进一步发展了一种傅里叶变换方法来处理变量选择、分类预测变量以及大的p，小的n数据。为了检验维度，得到了渐近的结果。仿真研究和数据分析表明了该方法的有效性。
ABSTRACT Estimating an inverse regression space is especially important in sufficient dimension reduction. However, it typically requires a tuning parameter, such as the number of slices in a slicing method or bandwidth selection in a kernel estimation approach. Such a requirement not only affects the accuracy of estimates in a finite sample, but also increases difficulties for multivariate models. In this paper, we use a Fourier transform approach to avoid such difficulties and incorporate multivariate models. We further develop a Fourier transform approach to deal with variable selection, categorical predictor variables, and large p, small n data. To test the dimension, asymptotic results are obtained. Simulation studies and data analysis show the efficacy of our proposed methods.