DATA-BASED BANDWIDTH SELECTION FOR KERNEL ESTIMATORS OF THE INTEGRAL OF F(2)(X)

A review of different density estimation approaches to estimating gamm a = integral(-infinity)(infinity)integral(2)(x)dx is given. A plug-in approach to bandwidth selection is developed for kernel estimators of gamma. The resulting data-based bandwidths have relative rate of conve rgence of order n(-1/2), which is the best possible. Finally, we repor t the results of a Monte Carlo study that indicate that the overall pe rformance of a kernel estimator of gamma based on the plug-in bandwidt h is better than that of two other popular estimators of gamma, at lea st when the sample size is 40 or more.