Vol. 9, No. 1, 2014

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
On inference of statistical regression models for extreme events based on incomplete observation data

Olga Kaiser and Illia Horenko

Vol. 9 (2014), No. 1, 143–174
Abstract

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.

Keywords
generalized extreme-value distribution, systematically missing information, nonstationary time-series analysis, nonparametric statistics, finite-element method
Mathematical Subject Classification 2010
Primary: 62G05, 62G32, 65R32
Secondary: 65C50, 62F03
Milestones
Received: 20 May 2013
Revised: 28 November 2013
Accepted: 31 March 2014
Published: 25 May 2014
Authors
Olga Kaiser
Institute of Computational Science
Università della Svizzera italiana
Via Giuseppe Buffi 13
CH-6904 Lugano
Switzerland
Illia Horenko
Institute of Computational Science
Università della Svizzera italiana
Via Giuseppe Buffi 13
CH-6904 Lugano
Switzerland