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Fast computation of large scale marginal extremes with multi-dimensional covariates

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  • Raghupathi, Laks
  • Randell, David
  • Ewans, Kevin
  • Jonathan, Philip

Abstract

Safe and reliable design and operation of fixed and floating marine structures often located in remote and hostile environments is challenging. Rigorous extreme value analysis of meteorological and oceanographic data can greatly aid the design of such structures. Extreme value analysis is typically undertaken for single spatial locations or for small neighbourhoods; moreover, non-stationary effects of covariates on extreme values are typically accommodated in an ad-hoc manner. The objective of the work summarised here is to improve design practice by estimating environmental design conditions (such as return values for extreme waves, winds and currents) for a whole ocean basin, including additional covariate effects (such as storm direction) as necessary, in a consistent manner. Whole-basin non-stationary extreme value modelling is computationally complex, requiring inter-alia the estimation of tail functions, the parameters of which vary with respect to multi-dimensional covariates characterised by us using tensor products of penalised B-splines. We outline two technical contributions which make whole-basin non-stationary analysis feasible. Firstly, we adopt generalised linear array methods to reduce the computational burden of matrix manipulations. Secondly, using high-performance computing, we develop a parallel implementation of maximum likelihood estimation for the generalised Pareto distribution. Together, these innovations allow estimation of rigorous whole-basin extreme value models in reasonable time. We evaluate the new approach in application to marginal extreme value modelling of storm peak significant wave heights in two ocean basins, accommodating spatial and directional covariate effects.

Suggested Citation

  • Raghupathi, Laks & Randell, David & Ewans, Kevin & Jonathan, Philip, 2016. "Fast computation of large scale marginal extremes with multi-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 243-258.
    • Handle: RePEc:eee:csdana:v:95:y:2016:i:c:p:243-258
    DOI: 10.1016/j.csda.2015.09.006
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    References listed on IDEAS

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    1. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280, April.
    2. V. Chavez‐Demoulin & A. C. Davison, 2005. "Generalized additive modelling of sample extremes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 207-222, January.
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    Cited by:

    1. E. Zanini & E. Eastoe & M. J. Jones & D. Randell & P. Jonathan, 2020. "Flexible covariate representations for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.

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