CONVERGENCE OF KERNEL FUNCTIONS FOR CUBIC SMOOTHING SPLINES ON NON‐EQUISPACED GRIDS

Abstract

summaryNumerical experimentation with data, which is quite noisy and on a highly non‐even grid, shows that cubic smoothing splines give a visually pleasing fit to the data, even when the interpolating spline oscillates wildly. In part, Silverman (1984) has explained this fact by showing that the cubic smoothing spline converges, to a certain kernel approximation as the number of data points is increased. In this paper, we examine the convergence of the kernel functions which generate the cubic smoothing spline fit to data, under weaker conditions on the non‐even grid than imposed by Silverman.