Fourier transform approach for inverse dimension reduction method. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Weng, Jiaying; Yin, Xiangrong
• Is Part Of: Journal of nonparametric statistics. Volume 30:Issue 4(2018)
• Page Start: 1049
• Page End: 1071
• Publication Date: 2018-10-02
• Subjects: Central subspaces -- Fourier transform -- Inverse regression -- Sufficient dimension reduction; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2018.1515432
• Languages: English
• ISSNs: 1048-5252

Abstract

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.