Abstract
The Efron-Stein inequality is applied to prove that the kernel density estimate $f_n$, with an arbitrary nonnegative kernel and an arbitrary smoothing factor, satisfies the inequality $\operatorname{var}(\int|f_n - f|) \leq 4/n$ for all densities $f$. Similar inequalities are obtained for other estimates.
Citation
Luc Devroye. "An Application of the Efron-Stein Inequality in Density Estimation." Ann. Statist. 15 (3) 1317 - 1320, September, 1987. https://doi.org/10.1214/aos/1176350508
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