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Fourier transform approach for inverse dimension reduction method

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  • Jiaying Weng
  • Xiangrong Yin

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.

Suggested Citation

  • Jiaying Weng & Xiangrong Yin, 2018. "Fourier transform approach for inverse dimension reduction method," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(4), pages 1049-1071, October.
    • Handle: RePEc:taf:gnstxx:v:30:y:2018:i:4:p:1049-1071
    DOI: 10.1080/10485252.2018.1515432
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    Cited by:

    1. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. S. Yaser Samadi & Tharindu P. De Alwis, 2023. "Fourier Methods for Sufficient Dimension Reduction in Time Series," Papers 2312.02110, arXiv.org.

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