We present a computationally efficient, semiparametric, nonstationary framework for
statistical regression analysis of extremes with systematically missing covariates
based on the generalized extreme value (GEV) distribution. It is shown that the
involved regression model becomes nonstationary if some of the relevant model
covariates are systematically missing. The resulting nonstationarity and the
ill-posedness of the inverse problem are resolved by deploying the recently introduced
finite-element time-series analysis methodology with bounded variation of model
parameters (FEM-BV). The proposed FEM-BV-GEV approach allows a well-posed
problem formulation and goes beyond probabilistic a priori assumptions of
methods for analysis of extremes based on, e.g., nonstationary Bayesian
mixture models, smoothing kernel methods or neural networks. FEM-BV-GEV
determines the significant resolved covariates, reveals directly their influence
on the trend behavior in probabilities of extremes and reflects the implicit
impact of missing covariates. We compare the FEM-BV-GEV approach to the
state-of-the-art GEV-CDN methodology (based on artificial neural networks) on
test cases and real data according to four criteria: (1) information content
of the models, (2) robustness with respect to the systematically missing
information, (3) computational complexity and (4) interpretability of the
models.