TY - JOUR
T1 - Edgeworth expansion for the kernel quantile estimator
AU - Maesono, Yoshihiko
AU - Penev, Spiridon
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/6
Y1 - 2011/6
N2 - Using the kernel estimator of the pth quantile of a distribution brings about an improvement in comparison to the sample quantile estimator. The size and order of this improvement is revealed when studying the Edgeworth expansion of the kernel estimator. Using one more term beyond the normal approximation significantly improves the accuracy for small to moderate samples. The investigation is nonstandard since the influence function of the resulting L-statistic explicitly depends on the sample size. We obtain the expansion, justify its validity and demonstrate the numerical gains in using it.
AB - Using the kernel estimator of the pth quantile of a distribution brings about an improvement in comparison to the sample quantile estimator. The size and order of this improvement is revealed when studying the Edgeworth expansion of the kernel estimator. Using one more term beyond the normal approximation significantly improves the accuracy for small to moderate samples. The investigation is nonstandard since the influence function of the resulting L-statistic explicitly depends on the sample size. We obtain the expansion, justify its validity and demonstrate the numerical gains in using it.
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U2 - 10.1007/s10463-009-0241-5
DO - 10.1007/s10463-009-0241-5
M3 - Article
AN - SCOPUS:79960088380
SN - 0020-3157
VL - 63
SP - 617
EP - 644
JO - Annals of the Institute of Statistical Mathematics
JF - Annals of the Institute of Statistical Mathematics
IS - 3
ER -