Fixed-k Inference for Conditional Extremal Quantiles

Yuya Sasaki, Yulong Wang

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
JournalJournal of Business and Economic Statistics
DOIs
StateAccepted/In press - 2021

Keywords

  • Conditional extremal quantile
  • Confidence interval
  • Extreme value theory
  • Fixed k
  • Random coefficient

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

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