The estimate of error standard deviation in nonparametric regression is used to obtain confidence intervals for the unknown curve and to estimate the bandwidth or smoothing parameter. In this paper we report on an extensive simulation study comparing the finite sample properties of several estimators of the error standard deviation when the unknown function is estimated by spline smoothing with the smoothing parameter estimated by both generalized cross-validation and marginal likelihood. The performance of the estimators is also compared to the nonparametric estimators of Rice (1984) and Gasser, Sroka and Jennen-Steinmetz (1986). On the basis of statistical and computational efficiency the paper recommends the marginal likelihood estimator using quintic splines, although several other estimators have similar finite sample performance but require more computation.
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