Two Cross Validation Criteria for SIR<Subscript>α</Subscript> and PSIR<Subscript>α</Subscript> methods in view of prediction

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<Subscript>α</Subscript> and PSIR<Subscript>α</Subscript>. 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