Devroye, Luc An application of the Efron-Stein inequality in density estimation. (English) Zbl 0631.62039 Ann. Stat. 15, 1317-1320 (1987). 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 var(\(\int | f_ n- f|)\leq 4/n\) for all densities f. Similar inequalities are obtained for other estimates. Cited in 1 Document MSC: 62G05 Nonparametric estimation 60E15 Inequalities; stochastic orderings 62G15 Nonparametric tolerance and confidence regions Keywords:distribution-free confidence interval; Efron-Stein inequality; kernel density estimate; arbitrary nonnegative kernel; arbitrary smoothing factor × Cite Format Result Cite Review PDF Full Text: DOI