Interpolation Methods for Adapting to Sparse Design in Nonparametric Regression

We suggest interpolation methods for overcoming the problem of sparse design in local linear smoothing. These methods are based on simple rules, determined by the kernel and bandwidth, for deciding when and where pseudo-design points should be added to augment the original design sequence. New ordinates for the added design points are computed by simple interpolation, then local linear smoothing is applied directly to the expanded dataset. The method is competitive with alternatives (e.g., those involving ridge regression), in terms of both simplicity and performance.