A NEW CLASS OF KERNELS FOR NONPARAMETRIC CURVE ESTIMATION

We introduce a new class of variable kernels which depend on the smoot hing parameter b through a simple scaling operation, and which have go od integrated mean square error (IMSE) convergence properties. These k ernels deform ''automatically'' near the boundary, eliminating boundar y bias. Computational formulas are given for all orders of kernel in t erms of exponentially damped sines and cosines. The kernel is a comput ationally convenient approximation to a certain Green's function, with the resulting kernel estimate closely related to a smoothing spline e stimate.