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Asymptotics for kernel estimate of sliced inverse regression. (English) Zbl 0864.62027
Summary: To explore nonlinear structures hidden in high-dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression, N. Duan and K. C. Li [ibid. 19, No. 2, 505-530 (1991; Zbl 0738.62070)] proposed the sliced inverse regression (SIR) method which is simple to use. In this paper, the asymptotic properties of the kernel estimate of sliced inverse regression are investigated. It turns out that regardless of the kernel function, the asymptotic distribution remains the same for a wide range of smoothing parameters.

62G07Density estimation
62G20Nonparametric asymptotic efficiency
62E20Asymptotic distribution theory in statistics
62J02General nonlinear regression