Fixed-k Inference for Conditional Extremal Quantiles

TL;DR

This paper introduces a new method for constructing confidence intervals for conditional extremal quantiles using a fixed number of tail observations, applicable to cross-sectional and panel data, with improved small-sample performance.

Contribution

It develops a novel extreme value theory for fixed-k tail observations, enabling valid nonparametric inference for extremal quantiles without parametric assumptions.

Findings

Confidence intervals have superior coverage and length properties in simulations.

Method applied to birth weight data confirms known effects with different magnitudes.

Provides a new tool for extremal quantile inference in various data settings.

Abstract

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.