The authors 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, they 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 the authors' 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, the authors study factors of extremely low birth weights. They find that signs of major effects are the same as those found in preceding studies based on parametric models, but with different magnitudes.