Abstract
We use the probabilistic method to show that if $f_{nh}$ is the standard kernel estimate with smoothing factor $h$, then there exists a deterministic sequence $h_n$ such that, for all densities, $\operatornamewithlimits{\lim\inf}_{n\rightarrow\infty} \frac{\mathbf{E} \int |f_{nh_n} - f|}{\inf_h \mathbf{E} \int |f_{nh} - f|} = 1.$
Citation
Luc Devroye. "On Good Deterministic Smoothing Sequences for Kernel Density Estimates." Ann. Statist. 22 (2) 886 - 889, June, 1994. https://doi.org/10.1214/aos/1176325500
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