On inference of statistical regression models for extreme events based on incomplete observation data. (English) Zbl 1328.62209

Kaiser, Olga; Horenko, Illia

Commun. Appl. Math. Comput. Sci. 9, No. 1, 143-174 (2014).

Summary: 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.

MSC:

62G05	Nonparametric estimation
62G32	Statistics of extreme values; tail inference
65R32	Numerical methods for inverse problems for integral equations
65C50	Other computational problems in probability (MSC2010)
62F03	Parametric hypothesis testing

Keywords:

generalized extreme-value distribution; systematically; missing information; nonstationary time-series analysis; nonparametric statistics; finite-element method