Universal Consistency of Local Polynomial Kernel Regression Estimates

Regression function estimation from independent and identically distributed data is considered. The L2 error with integration with respect to the design measure is used as an error criterion. It is shown that suitably defined local polynomial kernel estimates are weakly and strongly universally consistent, i.e., it is shown that the L2 errors of these estimates converge to zero almost surely and in L1 for all distributions.