a1 Dept. of Statistics, Institute of Advanced Studies, Australian National University, GPO Box 4, Canberra, A.C.T. 2601, Australia.
a2 Dept. of Pure and Applied Mathematics, Washington State University, Pullman 99164-2930, WA, USA.
We consider a generalisation of the stochastic formulation of smoothing splines, and discuss the smoothness properties of the resulting conditional expectation (generalised smoothing spline), and the sensitivity of the numerical algorithms. One application is to the calculation of smoothing splines with less than the usual order of continuity at the data points.
(Received July 29 1986)
(Revised June 04 1987)