A Boundary Modification of Kernel Function Smoothing, with Application to Insulin Absorption Kinetics

Kernel function smoothing of observations lying around a regression function is a procedure with marked boundary effects and therefore specific consideration of boundary problems is important. A traditional solution is the construction of kernels designed specifically for use at the boundary. These are derived assuming that the design is continuous. The problem is solved for minimum variance kernels, but not for optimal kernels. In practice, the design is discrete and the boundary kernels may give large variance and biased results even for linear functions. A new procedure, the so-called time-adjustment is proposed. This procedure can be applied to estimates both with and without boundary modifications and is an improvement in both cases.