White noise models often renormalize exactly yielding optimal rates of convergence for pointwise nonparametric functional estimation problems. Similar rescaling ideas lead to a sequence of experiments appropriate for pointwise density estimation problems.
"Renormalization and White Noise Approximation for Nonparametric Functional Estimation Problems." Ann. Statist. 20 (1) 545 - 554, March, 1992. https://doi.org/10.1214/aos/1176348538