A Cross-Validatory Choice of Smoothing Parameter in Adaptive Location Estimation

Abstract

This article proposes a new data-driven method for selecting the smoothing parameter involved in the construction of kernel-based adaptive location estimators. The method consists of minimizing a cross-validatory criterion with respect to the bandwidth occurring in the kemd type estimators of the efficient score function. It is shown that the location estimator with a data-driven bandwidth selector is indeed an adaptive estimator. A simulation study is conducted and it reveals that the method is also practicable, showing that our estimator performs well in comparison with some other well-known location estimators. It also shows that our method has comparable finite sample performance with the bootstrap method of selecting the smoothing parameter, and yet has great computational advantages.