A graphical method for estimating the residual variance in nonparametric regression

If one wishes to make inferences about a regression, then an accurate estimator of the residual variance is required. However, except in the simplest cases, all estimators of variance are biased by an amount which depends on the unknown regression. Here, a graphical procedure is proposed which indicates whether the bias in a particular estimate is small. This procedure is studied in some detail for estimators which are weighted sums of squares of divided differences of the data and leads to a practical method of variance estimation.