Smoothing by Local Regression

A kernal smoother is an intuitive estimate of a regression function or conditional expectation; at each year X sub 0 the estimate of E (Y | X sub 0) is a weighted mean of the sample Y sub i, where the weights, given by the kernal, die down smoothly with || X sub i - X sub 0||. Unfortunately this simplicity has flaws. At a boundary of X, the kernal neighborhood is asymmetric and the estimate may have substantial bias.