ASYMPTOTIC EQUIVALENCE OF NONPARAMETRIC REGRESSION AND WHITE-NOISE

The principal result is that, under conditions, to any nonparametric r egression problem there corresponds an asymptotically equivalent seque nce of white noise with drift problems, and conversely. This asymptoti c equivalence is in a global and uniform sense. Any normalized risk fu nction attainable in one problem is asymptotically attainable in the o ther, with the difference in normalized risks converging to zero unifo rmly over the entire parameter space. The results are constructive. A recipe is provided for producing these asymptotically equivalent proce dures. Some implications and generalizations of the principal result a re also discussed.