Local likelihood estimation of complex tail dependence structures, applied to U.S. precipitation extremes

To disentangle the complex non-stationary dependence structure of precipitation extremes over the entire contiguous U.S., we propose a flexible local approach based on factor copula models. Our sub-asymptotic spatial modeling framework yields non-trivial tail dependence structures, with a weakening dependence strength as events become more extreme, a feature commonly observed with precipitation data but not accounted for in classical asymptotic extreme-value models. To estimate the local extremal behavior, we fit the proposed model in small regional neighborhoods to high threshold exceedances, under the assumption of local stationarity, which allows us to gain in flexibility. Adopting a local censored likelihood approach, inference is made on a fine spatial grid, and local estimation is performed by taking advantage of distributed computing resources and the embarrassingly parallel nature of this estimation procedure. The local model is efficiently fitted at all grid points, and uncertainty is measured using a block bootstrap procedure. An extensive simulation study shows that our approach can adequately capture complex, non-stationary dependencies, while our study of U.S. winter precipitation data reveals interesting differences in local tail structures over space, which has important implications on regional risk assessment of extreme precipitation events

Gaussian semiparametric estimates on the unit sphere

We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate maximum likelihood estimator and we investigate its asympotic weak consistency and Gaussianity, in both parametric and semiparametric cases.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ475 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm