Nonparametric density and regression estimators commonly depend on abandwidth. The asymptotic properties of these estimators have been widelystudied when bandwidths are nonstochastic. In practice, however, in order toimprove finite sample performance of these estimators, bandwidths are selectedby data driven methods, such as cross-validation or plug-in procedures. As aresult nonparametric estimators are usually constructed using stochasticbandwidths. In this paper we establish the asymptotic equivalence inprobability of local polynomial regression estimators under stochastic andnonstochastic bandwidths. Our result extends previous work by Boente andFraiman (1995) and Ziegler (2004).
展开▼
