The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives*
证明在半参数指数模型的密度加权平均导数估计中，自助法分布能实现有效的埃奇沃思修正，并讨论偏差缩减方法，通过Tobit模型的蒙特卡洛模拟考察有限样本表现。
In a number of semiparametric models, smoothing seems necessary in order to obtain estimates of the parametric component which are asymptotically normal and converge at parametric rate. However, smoothing can inflate the error in the normal approximation, so that refined approximations are of interest, especially in sample sizes that are not enormous. We show that a bootstrap distribution achieves a valid Edgeworth correction in the case of density-weighted averaged derivative estimates of semiparametric index models. Approaches to bias reduction are discussed. We also develop a higher-order expansion to show that the bootstrap achieves a further reduction in size distortion in the case of two-sided testing. The finite-sample performance of the methods is investigated by means of Monte Carlo simulations from a Tobit model. Copyright The Econometric Society 2005.