Derivation of equivalent kernel for general spline smoothing: A system approach (Q1290381)

Spline smoothing for estimating regression functions is considered. The authors extend results about equivalent kernels in two directions -- arbitrary design densities and variable smoothing parameters are included. It is shown that also in this more general case the equivalent kernels can be approximated by the Green functions of certain linear differential operators. A standard method, known as the Wentzel-Kramers-Brillouin method, for the systematic derivation of asymptotically equivalent kernels is proposed. Furthermore, the problem of finding equivalent kernels for general \(L\)-spline smoothing is considered.