On a weighted bootstrap approximation of the LpLp norms of kernel density estimators

A weighted bootstrap method is considered to approximate the distribution of the LpLp norms of kernel density estimates. Here pp is any number in [1,∞)[1,∞). Using a Komlós–Major–Tusnády type approximation (Komlós et al., 1975) for weighted bootstrap processes, due to Horváth et al. (2000), we establish unconditional bootstrap central limit theorems for these LpLp statistics.