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Edgeworth expansions for semiparametric averaged derivatives

By Y Nishiyama and Peter Robinson

Abstract

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

Topics: HB Economic Theory
Publisher: Wiley-Blackwell on behalf of the Econometric Society
Year: 2000
DOI identifier: 10.1111/1468-0262.00142
OAI identifier: oai:eprints.lse.ac.uk:1304
Provided by: LSE Research Online
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