Influence diagnostics and model validation for the generalized extreme-value nonlinear regression model

ABSTRACT

Extreme-value theory is useful for modelling extremal events. The behaviour of such extremal events may be impacted by other variables and such dependence is captured using a regression framework. In this paper, we develop residual based diagnostic analysis, generalized leverage, generalized Cook's distance and also global and local influence analysis for the generalized extreme-value nonlinear regression model. Two residuals for use with the model are proposed: the standardized and deviance residuals. Additionally, we present a model misspecification test that can be used to determine whether the fitted model is incorrectly specified. We also show how to perform nonnested testing inferences. Empirical applications based on simulated and observed data are presented and discussed.

KEYWORDS:

• Extreme value
• generalized extreme-value regression
• Gumbel distribution
• local influence
• misspecification test

Acknowledgements

We gratefully acknowledge partial financial support from CAPES and CNPq. We also thank an anonymous referee for comments, corrections and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico [grants number 301651/2017-5 and 305336/2017-7].