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A two-step approach to model precipitation extremes in California based on max-stable and marginal point processes
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 Ni\~{n}o-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 Ni\~{n}o effect, narrower
confidence intervals for return levels and tighter confidence regions for risk
measures of jointly defined events.Comment: Published at http://dx.doi.org/10.1214/14-AOAS804 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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Estimation with stable disturbances
textThe family of stable distributions represents an important generalization of the Gaussian family; stable random variables obey a generalized central limit theorem where the assumption of finite variance is replaced with one of power law decay in the tails. Possessing heavy tails, asymmetry, and infinite variance, non-Gaussian stable distributions can be suitable for inference in settings featuring impulsive, possibly skewed noise. A general lack of analytical form for the densities and distributions of stable laws has prompted research into computational methods of estimation. This report introduces stable distributions through a discussion of their basic properties and definitions in chapter 1. Chapter 2 surveys applications, and chapter 3 discusses a number of procedures for inference, with particular attention to time series models in the ARMA setting. Further details and an application can be found in the appendices.Statistic
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