Summary
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 SIRα and PSIRα. 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.
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Acknowledgements
The authors are grateful to the Editor, the Associate Editor and two anonymous referees for contributing to the improvement of this paper through many useful remarks and suggestions and detailed comments. We like to thank Pr. Simon Thacker from Rochambau School whose remarks led to an important improvement of the presentation.
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Gannoun, A., Saracco, J. Two Cross Validation Criteria for SIRα and PSIRα methods in view of prediction. Computational Statistics 18, 585–603 (2003). https://doi.org/10.1007/BF03354618
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DOI: https://doi.org/10.1007/BF03354618