Friedman’s Super Smoother

Friedman’s super smoother is a nonparametric regression estimator based on local linear regression with adaptive bandwidths (Friedman [1984]). The basic idea is to first estimate a number of fixed bandwidth smooths by local linear regression. The leave-one-out cross-validated residuals from each of those initial estimates are then smoothed using a constant bandwidth. Based on the smoothed residuals, the best bandwidths from the initial estimates are selected at each data point over the range of the predictor variable. Those local bandwidths are then smoothed with a constant bandwidth, and the two estimates from the initial estimates with closest bandwidth values to the smoothed bandwidths are selected, and the smoothed outcomes are linearly interpolated. The interpolated points are then smoothed again with a fixed bandwidth, resulting in the final estimate.