Nishiyama, Y and Robinson, Peter M. (1999) Edgeworth expansions for semiparametric averaged derivatives. Econometrics; EM/1999/373, EM/99/373. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.
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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 -½ that prevails in standard parametric problems, but we find circumstances in which it is O(n -½), thereby extending the achievement of an n -½ Berry-Essen bound in Robinson (1995). A valid empirical Edgeworth expansion is also established. We also provide theoretical and empirical Edgeworth expansions for a studentized statistic, where the correction terms are different from those for the unstudentized case. We report a Monte Carlo study of finite sample performance.
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