Higher-Order Asymptotic Properties of Kernel Density Estimator with Plug-In Bandwidth

Shunsuke Imai () and Yoshihiko Nishiyama ()
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Shunsuke Imai: Faculty of Economics, Kyoto University, JAPAN
Yoshihiko Nishiyama: Institute of Economic Research, Kyoto University, JAPAN,

No 1076, KIER Working Papers from Kyoto University, Institute of Economic Research

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.

Keywords: nonparametric statistics; kernel density estimator; plug-in bandwidth; Edgeworth expansion (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2022-03
New Economics Papers: this item is included in nep-ecm
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