Simple Edgeworth approximations for semiparametric averaged derivatives

This note proposes a computationally simple empirical Edgeworth expansion for the limiting distribution of a Studentized estimator of a semiparametric single index model. The estimator in question is the density-weighted averaged derivative estimator implemented according to the method of Powell, Stock and Stoker (1989). The coefficients of the expansion are derived from the cumulants of a bootstrap estimate of the distribution of the Studentized estimator. Monte Carlo evidence indicates finite-sample performance comparable to that of the empirical Edgeworth expansions proposed by Nishiyama and Robinson (2000).