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Two Cross Validation Criteria for SIR α and PSIR α methods in view of prediction

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  • Ali Gannoun
  • Jérôme Saracco

Abstract

In this paper, we will consider the semiparametric regression model introduced by Duan and Li (1991). The response variable y will be linked to an index x′β (i.e. a linear combination of the explanatory variables x) through an unknown function. In order to estimate the direction of the unknown slope parameter β, Slicing and Pooled Slicing methods have been developed (see Duan and Li (1991), Li (1991), Aragon and Saracco (1997), Saracco (2001)). All the methods are computationally simple and fast. Among these methods, we focus on SIR α and PSIR α . We propose two cross validation criteria to select the parameter α. The evaluation of these criteria requires the kernel smoothing estimation of the link function. The choice of α is illustrated with simulations. Copyright Physica-Verlag 2003

Suggested Citation

  • Ali Gannoun & Jérôme Saracco, 2003. "Two Cross Validation Criteria for SIR α and PSIR α methods in view of prediction," Computational Statistics, Springer, vol. 18(3), pages 585-603, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:585-603
    DOI: 10.1007/BF03354618
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    References listed on IDEAS

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    1. Efstathia Bura & R. Dennis Cook, 2001. "Estimating the structural dimension of regressions via parametric inverse regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 393-410.
    2. Aragon, Y. & Saracco, J., 1996. "Sliced Inverse Regression (SIR): An Appraisal of Small Sample Alternatives to Slicing," Papers 95.392, Toulouse - GREMAQ.
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    Cited by:

    1. Zhu, Li-Xing & Ohtaki, Megu & Li, Yingxing, 2007. "On hybrid methods of inverse regression-based algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2621-2635, February.

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