  We determine the expected error by smoothing the data locally. Then we
optimize the shape of the kernel smoother to minimize the error. Because the
optimal estimator depends on the unknown function, our scheme automatically
adjusts to the unknown function. By self-consistently adjusting the kernel
smoother, the total estimator adapts to the data.
  Goodness of fit estimators select a kernel halfwidth by minimizing a function
of the halfwidth which is based on the average square residual fit error:
$ASR(h)$. A penalty term is included to adjust for using the same data to
estimate the function and to evaluate the mean square error. Goodness of fit
estimators are relatively simple to implement, but the minimum (of the goodness
of fit functional) tends to be sensitive to small perturbations. To remedy this
sensitivity problem, we fit the mean square error %goodness of fit functional
to a two parameter model prior to determining the optimal halfwidth.
  Plug-in derivative estimators estimate the second derivative of the unknown
function in an initial step, and then substitute this estimate into the
asymptotic formula.
