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Edgeworth Expansions for Semiparametric Averaged Derivatives
Author(s) -
Nishiyama Y.,
Robinson P. M.
Publication year - 2000
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00142
Subject(s) - edgeworth series , studentized range , mathematics , statistic , monte carlo method , term (time) , limit (mathematics) , parametric statistics , statistics , econometrics , mathematical analysis , standard error , physics , quantum mechanics
A valid Edgeworth expansion is established for the limit distribution of density‐weighted semiparametric averaged derivative estimates of single index models. The leading term that corrects the normal limit varies in magnitude, depending on the choice of bandwidth and kernel order. In general this term has order larger than the n −1/2 that prevails in standard parametric problems, but we find circumstances in which it is O ( n −1/2 ), thereby extending the achievement of an n −1/2 Berry‐Esseen bound in Robinson (1995a). A valid empirical Edgeworth expansion is also established. We also provide theoretical and empirical Edgeworth expansions for a studentized statistic, where some correction terms are different from those for the unstudentized case. We report a Monte Carlo study of finite sample performance.