# Threshold modelling of spatially dependent non‐stationary extremes with application to hurricane‐induced wave heights

@article{Northrop2011ThresholdMO, title={Threshold modelling of spatially dependent non‐stationary extremes with application to hurricane‐induced wave heights}, author={Paul Northrop and Philip Jonathan}, journal={Environmetrics}, year={2011}, volume={22} }

In environmental applications it is common for the extremes of a variable to be non‐stationary, varying systematically in space, time or with the values of covariates. Multi‐site datasets are common, and in such cases there is likely to be non‐negligible inter‐site dependence. We consider applications in which multi‐site data are used to infer the marginal behaviour of the extremes at individual sites, while adjusting for inter‐site dependence. For reasons of statistical efficiency, it is…

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## References

SHOWING 1-10 OF 41 REFERENCES

Modelling non‐stationary extremes with application to surface level ozone

- Environmental Science
- 2009

It is suggested that the preprocessing method gives a model that better incorporates the underlying mechanisms that generate the process, produces a simpler and more efficient fit and allows easier computation.

Estimating extremes in climate change simulations using the peaks-over-threshold method with a non-stationary threshold

- Environmental Science
- 2010

Spatial Regression Models for Extremes

- Environmental Science, Mathematics
- 1999

Meteorological data are often recorded at a number of spatial locations. This gives rise to the possibility of pooling data through a spatial model to overcome some of the limitations imposed on an…

A Spatiodirectional Model for Extreme Waves in the Gulf of Mexico

- Environmental Science
- 2011

The characteristics of extreme waves in hurricane dominated regions vary systematically with a number of covariates, including location and storm direction. Reliable estimation of design criteria…

Bayesian Spatial Modeling of Extreme Precipitation Return Levels

- Environmental Science
- 2007

Quantification of precipitation extremes is important for flood planning purposes, and a common measure of extreme events is the r-year return level. We present a method for producing maps of…

Improved estimation for temporally clustered extremes

- Mathematics, Environmental Science
- 2007

Through a simulation study, it is demonstrated that the common practice of analysing peaks over thresholds (POT) is liable to incur serious bias in the estimation of parameters, as well as the return levels used as design specifications when building to withstand extremes of wind or rain, or river or sea level.

Regional Estimation from Spatially Dependent Data

- Environmental Science, Mathematics
- 2005

Regional estimation methods are used in such fields as hydrology and meteorology, for estimating parameters such as return values (or quantiles) of a distribution, when data are available at many…

Trend estimation in extremes of synthetic North Sea surges

- Environmental Science
- 2007

Summary. Mechanistic models for complex atmospheric and hydrological processes are often used to simulate extreme natural events, usually to quantify the risks that are associated with these events.…

Generalized additive modelling of sample extremes

- Environmental Science
- 2005

Summary. We describe smooth non‐stationary generalized additive modelling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. Fitting is…

Models for exceedances over high thresholds

- Mathematics
- 1990

We discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds. The natural distribution for such exceedances, the generalized Pareto…