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March 2015 A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes
Hongwei Shang, Jun Yan, Xuebin Zhang
Ann. Appl. Stat. 9(1): 452-473 (March 2015). DOI: 10.1214/14-AOAS804


In modeling spatial extremes, the dependence structure is classically inferred by assuming that block maxima derive from max-stable processes. Weather stations provide daily records rather than just block maxima. The point process approach for univariate extreme value analysis, which uses more historical data and is preferred by some practitioners, does not adapt easily to the spatial setting. We propose a two-step approach with a composite likelihood that utilizes site-wise daily records in addition to block maxima. The procedure separates the estimation of marginal parameters and dependence parameters into two steps. The first step estimates the marginal parameters with an independence likelihood from the point process approach using daily records. Given the marginal parameter estimates, the second step estimates the dependence parameters with a pairwise likelihood using block maxima. In a simulation study, the two-step approach was found to be more efficient than the pairwise likelihood approach using only block maxima. The method was applied to study the effect of El Niño-Southern Oscillation on extreme precipitation in California with maximum daily winter precipitation from 35 sites over 55 years. Using site-specific generalized extreme value models, the two-step approach led to more sites detected with the El Niño effect, narrower confidence intervals for return levels and tighter confidence regions for risk measures of jointly defined events.


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Hongwei Shang. Jun Yan. Xuebin Zhang. "A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes." Ann. Appl. Stat. 9 (1) 452 - 473, March 2015.


Published: March 2015
First available in Project Euclid: 28 April 2015

zbMATH: 06446576
MathSciNet: MR3341123
Digital Object Identifier: 10.1214/14-AOAS804

Keywords: Composite likelihood , estimating function , Extreme value analysis , risk analysis , spatial dependence

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.9 • No. 1 • March 2015
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