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On spline approximation of sliced inverse regression

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Abstract

The dimension reduction is helpful and often necessary in exploring the nonparametric regression structure. In this area, Sliced inverse regression (SIR) is a promising tool to estimate the central dimension reduction (CDR) space. To estimate the kernel matrix of the SIR, we herein suggest the spline approximation using the least squares regression. The heteroscedasticity can be incorporated well by introducing an appropriate weight function. The root-n asymptotic normality can be achieved for a wide range choice of knots. This is essentially analogous to the kernel estimation. Moreover, we also propose a modified Bayes information criterion (BIC) based on the eigenvalues of the SIR matrix. This modified BIC can be applied to any form of the SIR and other related methods. The methodology and some of the practical issues are illustrated through the horse mussel data. Empirical studies evidence the performance of our proposed spline approximation by comparison of the existing estimators.

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Authors and Affiliations

  1. Department of Statistics, East China Normal University, Shanghai, 200062, China

    Li-ping Zhu & Zhou Yu

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  1. Li-ping Zhu
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  2. Zhou Yu
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Correspondence to Li-ping Zhu.

Additional information

This work was supported by the special fund (2006) for selecting and training young teachers of universities in Shanghai (Grant No. 79001320) and an FRG grant (FRG/06-07/I-06) from Hong Kong Baptist University, China, and a grant (HKU 7058/05P) from the Research Grants Council of Hong Kong, China

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Zhu, Lp., Yu, Z. On spline approximation of sliced inverse regression. SCI CHINA SER A 50, 1289–1302 (2007). https://doi.org/10.1007/s11425-007-0085-5

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  • DOI: https://doi.org/10.1007/s11425-007-0085-5

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