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Title: Higher-Order Asymptotic Properties of Kernel Density Estimator with Plug-In Bandwidth
Authors: Imai, Shunsuke
Nishiyama, Yoshihiko
Keywords: C14
nonparametric statistics
kernel density estimator
plug-in bandwidth
Edgeworth expansion
Issue Date: Mar-2022
Publisher: Institute of Economic Research, Kyoto University
Journal title: KIER Discussion Paper
Volume: 1076
Start page: 1
End page: 37
Abstract: This study investigates the effect of bandwidth selection via plug-in method on the asymptotic structure of the nonparametric kernel density estimator. We find that the plug-in method has no effect on the asymptotic structure of the estimator up to the order of O{(nh₀)⁻¹/²} = O(n[-L/(2L+1)]) for a bandwidth h0 and any kernel order L. We also provide the valid Edgeworth expansion up to the order of O{(nh₀)⁻¹} and find that the plug-in method starts to have an effect from on the term whose convergence rate is O{(nh₀)⁻¹/²h₀} = O(n[−(L+1)/(2L+1)]). In other words, we derive the exact convergence rate of the deviation between the distribution functions of the estimator with a deterministic bandwidth and with the plug-in bandwidth. Monte Carlo experiments are conducted to see whether our approximation improves previous results.
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Appears in Collections:KIER Discussion Paper (English)

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