On variable bandwidth selection in local polynomial regression

The performances of data-driven bandwidth selection procedures in local pol ynomial regression are investigated by using asymptotic methods and simulat ion. The bandwidth selection procedures considered are based on minimizing 'prelimit' approximations to the! (conditional) mean-squared error (MSE) wh en the MSE is considered as a function of the bandwidth h. We first conside r approximations to the MSE that are based on Taylor expansions around h = 0 of the bias part of the MSE. These approximations lead to estimators of t he MSE that are accurate only for small bandwidths h. We also consider a bi as estimator which instead of using small h approximations to bias naively estimates bias as the difference of two local polynomial estimators of diff erent order and we show that this estimator performs well only for moderate to large h. We next define a hybrid bias estimator which equals the Taylor -expansion-based estimator for small h and the difference estimator for mod erate to large h. We find that the MSE estimator based on this hybrid bias estimator leads to a bandwidth selection procedure with good asymptotic and , for our Monte Carlo examples, finite sample properties.