  To disentangle the complex non-stationary dependence structure of
precipitation extremes over the entire contiguous U.S., we propose a flexible
local approach based on factor copula models. Our sub-asymptotic spatial
modeling framework yields non-trivial tail dependence structures, with a
weakening dependence strength as events become more extreme, a feature commonly
observed with precipitation data but not accounted for in classical asymptotic
extreme-value models. To estimate the local extremal behavior, we fit the
proposed model in small regional neighborhoods to high threshold exceedances,
under the assumption of local stationarity, which allows us to gain in
flexibility. Adopting a local censored likelihood approach, inference is made
on a fine spatial grid, and local estimation is performed by taking advantage
of distributed computing resources and the embarrassingly parallel nature of
this estimation procedure. The local model is efficiently fitted at all grid
points, and uncertainty is measured using a block bootstrap procedure. An
extensive simulation study shows that our approach can adequately capture
complex, non-stationary dependencies, while our study of U.S. winter
precipitation data reveals interesting differences in local tail structures
over space, which has important implications on regional risk assessment of
extreme precipitation events.
