Date of Completion

11-20-2013

Embargo Period

11-20-2013

Keywords

Extreme value analysis; Extreme-value copula; Extremal coefficient; Maxstable process; Parametric bootstrap; Spatial dependence.

Major Advisor

Jun Yan

Associate Advisor

Dipak K. Dey

Associate Advisor

Xuebin Zhang

Associate Advisor

Zhiyi Chi

Field of Study

Statistics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

Parametric max-stable processes are increasingly used to model spatial extremes. Since the dependence structure is specified for block maxima, the data used for inference are block maxima from all sites. To improve the estimation efficiency, we propose a two-step approach with composite likelihood that utilizes site-wise daily records in addition to block maxima. Besides the parameter estimation, there is no formal model checking and diagnosis method for spatial extremes modeling yet. Model diagnosis in practice has been informal and mostly based on visual checking tools such as residual plot and quantile-quantile plot. We proposed a goodness-of-fit test for max-stable processes based on the comparison between a nonparametric and a parametric estimator of the corresponding unknown multivariate Pickands dependence function.

The proposed two-step procedure separates the estimation of marginal parameters and dependence parameters into two steps. In a simulation study, the two-step approach was found to provide more efficient estimator for the parameters and return levels than the composite likelihood approach based on block maxima data only. We applied the method to the maximum daily winter precipitation from 36 sites in California over 55 years, and compared with the composite likelihood approach.

A class of goodness-of-fit tests is proposed given the fact that the dependence structure of a max-stable process is completely characterized by an extreme-value copula. The finite-sample performance of the tests is investigated in dimension 10 under the Smith, Schlather and geometric Gaussian models. An application of the tests to rainfall data is finally presented.

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