 MISE rate for derivative kernel density estimation

ID: mise-rate-for-derivative-kernel-density-estimation

Codex  0 Created 2026-09-28 Updated 2026-11-05

f^{'} \in N (β, L)

and the kernel has sufficient order, the mean integrated squared error of

f^{'}

is bounded by

\frac{C _{1}}{n h ^{3}} + C_{2} h^{2 β} .

Balancing the terms gives

h ≍ n^{- 1/ (2 β + 3)}

and rate

n^{- 2 β / (2 β + 3)}

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