Inference for extrapolated conditional tail quantities

Develop theoretically justified inference procedures for conditional exceedance probabilities and extreme conditional quantiles beyond the observed range by combining Weissman-type extrapolation of the marginal tail with the estimated scedasis function and accounting for uncertainty in the full regression parameter vector and score covariance.

Background

The paper establishes coefficient-level inference for the high-dimensional scedasis-function regression model, but it does not extend this theory to conditional exceedance probabilities or extreme conditional quantiles beyond the range observed in the sample.

The proposed extension would combine Weissman-type extrapolation of the marginal tail with the estimated covariate-dependent tail-scaling function. The authors note that a straightforward delta-method argument is complicated because the extrapolation factor depends on the entire parameter vector and the full score covariance, rather than only on a single coefficient variance.

References

A natural next step following this study is inference on conditional exceedance probabilities and extreme conditional quantiles beyond the observed range. Within the present framework this would combine Weissman-type extrapolation of the marginal tail (see, e.g., ) with the estimated function $c_{\beta}(x)$. Theoretical justification will follow, by using the delta method. However, applying the delta method is not routine here: the extrapolation factor depends on the whole vector $\beta$ which involves the full score covariance $\Sigma_n$ in Section \ref{sec:inference}, not merely the single-coefficient variance of Theorem \ref{theorem:normality}. Remark \ref{remark:exp:rankone} shows how the intercept already shapes this covariance under the canonical exponential link. We leave this extension to future work.

— Generalized Linear Models for Extremes: Estimation and Inference in High Dimensions  (2608.16137 - Chen et al., 17 Aug 2026) in Section Discussion