Free knot polynomial spline confidence intervals

Confidence intervals and point estimation for a regression function based on polynomial splines with free knot locations are proposed. We choose the number of knots by the GCV criteria. The estimate of knot locations and coefficients are obtained through a nonlinear least square solution that corresponds to the maximum likelihood estimate. Confidence intervals are then constructed based on the asymptotic distribution of the MLE. Average coverage probabilities and accuracy of the estimate are examined via simulation. This method seems to work well for smooth as well as unsmooth (discontinuous) underlying functions. It also performs well for small sample sizes. We apply the method to study the productivity of US banks. The corresponding analysis supports certain research hypotheses concerning the effect of federal policy on banking efficiency