Empirical-bias bandwidths for local polynomial nonparametric regression and density estimation

A data-based local bandwidth selector is proposed for nonparametric regression by local tting of polynomials. The estimator, called the empirical-bias bandwidth selector (EBBS), is rather simple and easily allows multivariate predictor variables and estimation of any order derivative of the regression function. EBBS minimizes an estimate of mean square error consisting of a squared bias term plus a variance term. The variance term used is exact, not asymptotic, though it involves the conditonal variance of the response given the predictors that must be estimated. The bias term is estimated empirically, not from an asymptotic expression. Thus, EBBS is similar to the \double smoothing" approach of HH ardle, Hall, and Marron, but is developed here for a far wider class of estimation problems than what those authors consider. EBBS is tested on simulated data and its performance seems quite satisfactory. Local polynomial smoothing of a histogram is a highly eeective technique for density estimation, and several of the examples involve density estimation by EBBS applied to binned data.