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An application of the Efron-Stein inequality in density estimation. (English) Zbl 0631.62039

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.

MSC:

62G05 Nonparametric estimation
60E15 Inequalities; stochastic orderings
62G15 Nonparametric tolerance and confidence regions
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