Residual information criterion for single-index model selections

We develop a residual information criterion (RIC) for single-index models using the residual log-likelihood approach. The proposed criterion selects both the smoothing parameter and explanatory variables. Thus, it is a general selection criterion that provides a unified approach to model selection across both parametric and nonparametric functions. Monte Carlo studies demonstrate that RIC performs satisfactorily except when the sample size is small and the signal-to-noise ratio is weak. An application of RIC is illustrated for marketing a new medical technology.