## The Annals of Applied Statistics

### A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes

#### Abstract

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.

#### Article information

Source
Ann. Appl. Stat., Volume 9, Number 1 (2015), 452-473.

Dates
First available in Project Euclid: 28 April 2015

https://projecteuclid.org/euclid.aoas/1430226100

Digital Object Identifier
doi:10.1214/14-AOAS804

Mathematical Reviews number (MathSciNet)
MR3341123

Zentralblatt MATH identifier
06446576

#### Citation

Shang, Hongwei; Yan, Jun; Zhang, Xuebin. A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes. Ann. Appl. Stat. 9 (2015), no. 1, 452--473. doi:10.1214/14-AOAS804. https://projecteuclid.org/euclid.aoas/1430226100

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#### Supplemental materials

• Additional simulation results and data analysis.: We provide a sandwich variance estimator, additional tables summarizing the simulation study and additional figures in analyzing the California precipitation data.