A Note on Bootstrap Moment Consistency for Semiparametric M-Estimation

摘要: Cheng and Huang (2010) have recently proven that the bootstrap is asymptotically consistent in estimating distribution of M-estimate Euclidean parameter. In this note, we provide a first theoretical study on moment estimates semiparametric models. Specifically, establish consistency parameter which immediately implies $t$-type confidence set. It worthy pointing out only additional cost to achieve beyond strengthen $L_1$ maximal inequality condition required latter $L_p$ for $p\geq 1$. The key technical tool deriving above results general multiplier developed note. These conclusions hold when infinite dimensional nuisance root-n consistent, apply broad class methods with exchangeable weights. Our theory illustrated celebrated Cox regression model.