Spatial aggregation and high quantile estimation applied to extreme precipitation

When estimating high quantiles and tail probabilities related to the distribution of a spatially aggregated continuous stochastic process, one needs to account for spatial dependence. A way to tackle this problem uses the areal coefficient recently analysed in [8] Ferreira, de Haan and Zhou (2012). We present new ways to estimate this spatial parameter and obtain asymptotic normality of the resulting quantile and tail probability estimators. Note that only consistency for the tail probability estimator was achieved in [8] mainly due to theoretical difficulties with the estimator of the areal coefficient therein considered.

Moreover, we evaluate the effect of the areal coefficient on return values, by an application to three case studies on precipitation extremes: North Holland, Venice Bay in Italy and Northwest Portugal. The proposed estimators seem to be a compromise, in the sense of being easier at a theoretical level and to apply but seem less effective in their performance when compared to the only existing alternative from [8].

In all we intend to draw attention to the areal coefficient. Though it is a unique number characterizing spatial dependence, it helps to explain in a simple way the differences usually observed when estimating quantiles (or tail probabilities) locally and from spatially aggregated data.

Keywords

extreme quantile and tail probability estimation, generalized Pareto distribution, spatial dependence, spatial aggregation, areal coefficient, extreme precipitation

2010 Mathematics Subject Classification

Primary 60G70, 62G32, 62M30. Secondary 62P12.

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Published 13 February 2015