A strong adaptive criteria is defined for density estimation problems. In a particular case it is shown that there is no strongly adaptive sequence of estimators. In contrast Woodroofe has shown that a weakly adaptive result holds.
"Non-Existence of an Adaptive Estimator for the Value of an Unknown Probability Density." Ann. Statist. 20 (1) 598 - 602, March, 1992. https://doi.org/10.1214/aos/1176348544