  We develop a new extreme value theory for repeated cross-sectional and 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.
