We introduce a multiplicative bias reducing estimator (MBRE) for nonparametric regression. We show that our estimator has optimal pointwise convergence rate n4/9, when positive kernels are used. A simulation study comparing our procedure with the higher order kernel method is included.

We propose a nonparametric multiplicative bias corrected transformation estimator designed for heavy tailed data. The multiplicative correction is based on prior knowledge and has a dimension reducing effect at the same time as the original dimension of the estimation problem is retained. Adding...