Zhu, Yu; Zeng, Peng Fourier methods for estimating the central subspace and the central mean subspace in regression. (English) Zbl 1171.62325 J. Am. Stat. Assoc. 101, No. 476, 1638-1651 (2006). Summary: In regression with a high-dimensional predictor vector, it is important to estimate the central and central mean subspaces that preserve sufficient information about the response and the mean response. Using the Fourier transform, we have derived the candidate matrices whose column spaces recover the central and central mean subspaces exhaustively. Under the normality assumption of the predictors, explicit estimates of the central and central mean subspaces are derived. Bootstrap procedures are used for determining dimensionality and choosing tuning parameters. Simulation results and an application to a real data are reported. Our methods demonstrate competitive performance compared with SIR, SAVE, and other existing methods. The approach proposed in the article provides a novel view on sufficient dimension reduction and may lead to more powerful tools in the future. Cited in 64 Documents MSC: 62G08 Nonparametric regression and quantile regression 65T60 Numerical methods for wavelets 62G09 Nonparametric statistical resampling methods 65C60 Computational problems in statistics (MSC2010) Keywords:bootstrap; candidate matrix; central mean subspace; central subspace; Fourier transform; SAVE; SIR PDFBibTeX XMLCite \textit{Y. Zhu} and \textit{P. Zeng}, J. Am. Stat. Assoc. 101, No. 476, 1638--1651 (2006; Zbl 1171.62325) Full Text: DOI