Bootstrapping density estimates
Let X1 X2…, Xn be independent and identically distributed random variables with continuous density function f(x) . Nonparametric density estimates of the form are considered. The asymptotic distribution of the sup over [0, 1] was obtained by Bickel and Rosenblatt (1973) and was used to construct confidence bands for f(x) . In this paper, confidence bands for f(x) based on bootstrap methods are considered and are shown to have the correct asymptotic level. The performance of bootstrap confidence bands is compared with the Bickel and Rosenblatt (1973) method by Monte Carlo simulation.