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Extreme value prediction via a quantile function model / Yuzhi Cai; Dominic Reeve

Coastal Engineering, Volume: 77

Swansea University Author: Cai, Yuzhi

Abstract

Methods for estimating extreme loads are used in design aswell as risk assessment. Regression usingmaximumlikelihood or least squares estimation is widely used in a univariate analysis but these methods favour solutionsthat fit observations in an average sense. Here we describe a new technique for e...

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Published in: Coastal Engineering
Published: 2013
URI: https://cronfa.swan.ac.uk/Record/cronfa15291
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Abstract: Methods for estimating extreme loads are used in design aswell as risk assessment. Regression usingmaximumlikelihood or least squares estimation is widely used in a univariate analysis but these methods favour solutionsthat fit observations in an average sense. Here we describe a new technique for estimating extremes using aquantile function model. A quantile of a distribution is most commonly termed a ‘return level’ in flood risk analysis.The quantile function of a randomvariable is the inverse function of its distribution function. Quantile functionmodels are different fromthe conventional regressionmodels, because a quantile function model estimatesthe quantiles of a variable conditional on some other variables, while a regressionmodel studies the conditionalmean of a variable. So quantile function models allowus to study thewhole conditional distribution of a variablevia its quantile function, whereas conventional regression models represent the average behaviour of a variable.Little work can be found in the literature about prediction froma quantile functionmodel. This paper proposes aprediction method for quantile functionmodels. We also compare different types of statistical models using sealevel observations from Venice. Our study shows that quantile function models can be used to estimate directlythe relationships between sea condition variables, and also to predict critical quantiles of a sea condition variableconditional on others. Our results show that the proposed quantile functionmodel and the developed predictionmethod have the potential to be very useful in practice.
Keywords: Extreme values Quantile function models Bayesian approach Semi-parametric model Parametric model Sea-level
College: School of Management
End Page: 98