Bootstrapping Kernel-Based Semiparametric Estimators

Abstract. This paper develops alternative asymptotic results for a large class of two-step semiparametric estimators. The \u85rst main result is an asymptotic distribution result for such estimators and di¤ers from those obtained in earlier work on classes of semiparametric two-step estimators by accommodating a non-negligible bias. A noteworthy feature of the assumptions under which the result is obtained is that reliance on a commonly employed stochastic equicontinuity condition is avoided. The second main result shows that the bootstrap provides an automatic method of correcting for the bias even when it is non-negligible