Kernel-Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency
研究了半参数估计量在非参数部分收敛速度较慢时的渐近分布，发现存在不可忽略的偏差，并证明某些自助法能自动校正该偏差，通过模拟验证了有限样本性质。
This paper develops asymptotic approximations for kernel-based semiparametric estimators under assumptions accommodating slower-than-usual rates of convergence of their nonparametric ingredients. Our first main result is a distributional approximation for semiparametric estimators that differs from existing approximations by accounting for a bias. This bias is nonnegligible in general, and therefore poses a challenge for inference. Our second main result shows that some (but not all) nonparametric bootstrap distributional approximations provide an automatic method of correcting for the bias. Our general theory is illustrated by means of examples and its main finite sample implications are corroborated in a simulation study.