A Risk Bound in Sobolev Class Regression
Sobolev 类回归中的风险界
For nonparametric regression estimation, when the unknown function belongs to a Sobolev smoothness class, sharp risk bounds for integrated mean square error have been found recently which improve on optimal rates of convergence results. The key to these has been the fact that under normality of the errors, the minimax linear estimator is asymptotically minimax in the class of all estimators. We extend this result to the nonnormal case, when the noise distribution is unknown.…