LOCALLY ADAPTIVE BANDWIDTH CHOICE FOR KERNEL REGRESSION-ESTIMATORS

Kernel estimators with a global bandwidth are commonly used to estimat e regression functions. On the other hand, it is obvious that the choi ce of a local bandwidth can lead to better results, because a larger c lass of kernel estimators is available. Evidently, this may in turn af fect variability. The optimal bandwidths depend essentially on the reg ression function itself and on the residual variance, and it is desira ble to estimate them from the data. In this article, a local bandwidth estimator is studied. A comparison with its global bandwidth equivale nt is performed both in theory and in simulations. As the main result it is shown that the possible gain in mean integrated squared error of the resulting regression estimator must be paid for by a larger varia bility of the estimator. This may lead to worse results if the sample size is small. An algorithm has been devised that puts special weight on stability aspects. Our simulation study shows that improvements ove r a global bandwidth estimator often can be realized even at small or moderate sample sizes.