Selection of the splined variables and convergence rates in a partial spline model

A method based on the principle of unbiased risk estimation is used to select the splined variables in an exploratory partial spline model proposed by Wahba (1985). The probability of correct selection based on the proposed procedure is discussed under regularity conditions. Furthermore, the resulting estimate of the regression function achieves the optimal rates of convergence over a general class of smooth regression functions (Stone 1982) when its underlying smoothness condition is not known.