ON THE CONSISTENCY OF CROSS-VALIDATION IN NONLINEAR WAVELET REGRESSION ESTIMATION

For the nonparametric regression model Yni =g(Xni) +εnii = 1, … n. with regulary spaced nonrandom design, the authors study the behavior of the nonlinear wavelet estimator of g(x). When the threshold and truncation parameters are chosen by crossvalidation on the everage squared error, strong consistency for the case of dyadic sample size and moment consistency for arbitrary sample size are established under some regular conditions.