We develop a new extreme value theory for  panel data to construct asymptotically valid confidence intervals (CIs) for conditional tail features such as conditional extreme quantile and conditional tail index . As a by-product, we also construct CIs for tail features of the coefficients in the random coefficient regression model. The new CIs are robustly valid without parametric assumptions and exhibit superior small sample coverage and length properties than alternative nonparametric approaches based on asymptotic normality. Applying the proposed method  , we study the tail risk of the monthly U. S. stock returns and find that (i) the left tail features of stock returns and those of the Fama-French regression residuals heavily depend on other stock characteristics such as stock size; and (ii) the alpha's and beta's are strongly heterogeneous across stocks in the Fama-French regression. These findings suggest that the Fama-French model may be insufficient to characterize the tail behavior of stock returns .
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 .
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repeated cross-sectional and
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tail features such as conditional extreme quantile and conditional tail index
extremal quantiles from a fixed number k of nearest-neighbor tail observations
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tail features of the coefficients in the random coefficient regression model. The new CIs are robustly
extremal quantiles of coefficients in linear random coefficient models. For any fixed k, the CIs are uniformly
R
and exhibit superior small sample
over a set of nonparametric data generating processes associated with various tail indices. Simulation studies show that our CIs exhibit superior small-sample
R
approaches
methods
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to Natality Vital Statistics
R
the tail risk of the monthly U. S. stock returns and find that (i) the left tail features of stock returns and those of the Fama-French regression residuals heavily depend on other stock characteristics such as stock size; and (ii) the alpha's and beta's are strongly heterogeneous across stocks in the Fama-French regression. These findings suggest that the Fama-French model may be insufficient to characterize the tail behavior of stock returns
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