Strong Universal Pointwise Consistency of Recursive Regression Estimates

摘要

For semi-recursive and recursive kernel estimates of a regression of Y on X (d-dimensional random vector X, integrable real random variable Y), introduced by Devroye and Wagner and by Révész, respectively, strong universal pointwise consistency is shown, i.e. strong consistency P X -almost everywhere for general distribution of (X, Y). Similar results are shown for the corresponding partitioning estimates.