Nishiyama, Yoshihiko: Edgeworth Expansions for Semiparametric Averaged Derivatives
World Conference Econometric Society, 2000, Seattle

Yoshihiko Nishiyama, Nagoya University
Peter M. Robinson, London School of Economics
Edgeworth Expansions for Semiparametric Averaged Derivatives
Session: C-9-15  Monday 14 August 2000  by Nishiyama, Yoshihiko
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 inverse of square root n that prevails in standard parametric problems, but we find circumstances in which it coincides with the parametric rate, thereby extending the achievement of a Berry-Esseen 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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