Edgeworth Expansions for Semiparametric Averaged Derivatives
为单指数模型的密度加权半参数平均导数估计建立了有效的埃奇沃思展开，发现修正项量级通常大于标准参数问题的n^{-1/2}，但在特定条件下可达到该阶数，并给出了学生化统计量的展开及蒙特卡洛模拟。
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.