AI 中文总结
针对半参数递归构造的一阶推断理论缺口，提出用结构残差经验分位数替代创新分位数的估计量，建立联合渐近线性表示，实现无需分位数平滑的无带宽推断。
AI 中文摘要
递归非线性脉冲响应要求在冲击按创新秩归一化且未来创新被积分时，需估计创新定律。文献中最接近的半参数递归构造平滑估计了相关创新分位数函数，并讨论了直接的经验残差实现，但未建立其完整的一阶推断理论。我们针对有限维非线性结构自回归模型（具有无限制的连续边际创新分布和固定的正态秩冲击）解决这一缺口。我们的估计量用生成的结构残差的经验分位数替代每个创新分位数函数，并迭代相同的结构转换。对于任意固定的响应集合，我们建立了含四个分量的联合√T渐近线性表示：直接转换估计、转换估计对残差顺序统计量的影响、普通创新分位数估计，以及移位的冲击分位数。经递归投影后，分位数项呈现残差秩与间距表示，从而无需创新密度估计或分位数平滑即可实现可行推断。随后，我们刻画了平滑带来的传播偏差，建立了完整递归残差自助法的有效性，并推导了有限数量模拟路径带来的额外协方差贡献，为平滑递归构造中使用的同一正态秩响应的经验残差版本提供了无带宽推断。
英文摘要
Recursive nonlinear impulse responses require an estimated innovation law whenever the impact shock is normalized by innovation ranks and future innovations are integrated out. The closest semiparametric recursive construction in the literature estimates the relevant innovation quantile functions smoothly and discusses a direct empirical-residual implementation without developing its complete first-order inference theory. We tackle this gap in a finite-dimensional nonlinear structural autoregression with unrestricted continuous marginal innovation distributions and a fixed normal-rank shock. Our estimator replaces each innovation quantile function with the empirical quantile of generated structural residuals and iterates the same structural transition. For any fixed collection of responses, we establish a joint \sqrt{T} asymptotic linear representation with four components: direct transition estimation, the effect of transition estimation on residual order statistics, ordinary innovation-quantile estimation, and the shifted impact quantile. After projection through the recursion, the quantile terms admit a residual-rank-and-spacing representation, yielding feasible inference without innovation-density estimation or quantile smoothing. We then characterize the propagated bias from smoothing, establish validity of a full recursive residual bootstrap, and derive the additional covariance contribution from a finite number of simulated paths, providing bandwidth-free inference for the empirical-residual version of the same normal-rank response used in the smooth recursive construction.
