Fixed-k Inference for Conditional Extremal Quantiles
提出一种新的极值理论，利用固定数量的尾部观测值构建条件极值分位数的置信区间，适用于重复截面与面板数据，模拟显示小样本表现优于传统非参数方法。
We develop a new extreme value theory for repeated cross-sectional and longitudinal/panel data to construct asymptotically valid confidence intervals (CIs) for conditional extremal quantiles from a fixed number k of nearest-neighbor tail observations. As a by-product, we also construct CIs for extremal quantiles of coefficients in linear random coefficient models. For any fixed k, the CIs are uniformly valid without parametric assumptions over a set of nonparametric data generating processes associated with various tail indices. Simulation studies show that our CIs exhibit superior small-sample coverage and length properties than alternative nonparametric methods based on asymptotic normality. Applying the proposed method to Natality Vital Statistics, we study factors of extremely low birth weights. We find that signs of major effects are the same as those found in preceding studies based on parametric models, but with different magnitudes.