ASSESSING PREDICTION ERROR IN NONPARAMETRIC REGRESSION

Recent development in the non-parametric regression method suggests th at the unknown optimal smoothing parameter derived from the conditiona l mean squared prediction error is very hard to estimate. We attempt t o provide some justification of this observation by showing that the p rediction error itself is almost impassible to estimate. In particular , the popular cross validation method fails to provide a reasonable es timate in the sense that the correlation coefficient between the predi ction error and its estimate is asymptotically negative and tends to z ero. The problem, however, is not with the cross validation method bec ause a similar result holds in the general regression setting regardle ss of the type of estimate and whether smoothing is involved or not.