Edgeworth Expansions for Semiparametric Averaged Derivatives
Econometrica · 2000 · Volume 68 · Issue 4
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 then−1/2that prevails in standard parametric problems, but we find circumstances in which it isO(n−1/2), thereby extending the achievement of ann−1/2Berry-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.
Keywords
Edgeworth expansion, semiparametric estimates, averaged derivatives.
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