Improved threshold diagnostic plots for extreme value analyses

Northrop, Paul J.; Coleman, Claire L.

doi:10.1007/s10687-014-0183-z

Cited by 45 publications

(48 citation statements)

References 11 publications

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“…Coles (2001) suggests to let the selection be guided by graphical diagnostics about bias (i.e., mean excess; see Ghosh and Resnick, 2010, for a detailed discussion) and stability of the scale and shape parameter. Despite these criteria being well justified from a theoretical point of view, their application involves substantial elements of subjectivity, leading to ambiguous results (Scarrott and MacDonald, 2012;Northrop and Coleman, 2014). To overcome this problem, we employed the deterministic squareroot rule k = √ n (Ferreira et al, 2003) for pre-selecting the threshold level in an objective way, using the kth upper-order statistic as a threshold, which is related to the total time series length n. Although this rule does not properly account for threshold uncertainty on subsequent inferences (Scarrot and MacDonald, 2012), it satisfies the intermediate sequence of order statistics that formally ensures tail convergence (Leadbetter et al, 1983).…”

Section: Threshold Excess Methodsmentioning

confidence: 99%

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Schlögl

Laaha

2017

Nat. Hazards Earth Syst. Sci.

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Abstract. The assessment of road infrastructure exposure to extreme weather events is of major importance for scientists and practitioners alike. In this study, we compare the different extreme value approaches and fitting methods with respect to their value for assessing the exposure of transport networks to extreme precipitation and temperature impacts. Based on an Austrian data set from 25 meteorological stations representing diverse meteorological conditions, we assess the added value of partial duration series (PDS) over the standardly used annual maxima series (AMS) in order to give recommendations for performing extreme value statistics of meteorological hazards. Results show the merits of the robust L-moment estimation, which yielded better results than maximum likelihood estimation in 62 % of all cases. At the same time, results question the general assumption of the threshold excess approach (employing PDS) being superior to the block maxima approach (employing AMS) due to information gain. For low return periods (non-extreme events) the PDS approach tends to overestimate return levels as compared to the AMS approach, whereas an opposite behavior was found for high return levels (extreme events). In extreme cases, an inappropriate threshold was shown to lead to considerable biases that may outperform the possible gain of information from including additional extreme events by far. This effect was visible from neither the square-root criterion nor standardly used graphical diagnosis (mean residual life plot) but rather from a direct comparison of AMS and PDS in combined quantile plots. We therefore recommend performing AMS and PDS approaches simultaneously in order to select the best-suited approach. This will make the analyses more robust, not only in cases where threshold selection and dependency introduces biases to the PDS approach but also in cases where the AMS contains non-extreme events that may introduce similar biases. For assessing the performance of extreme events we recommend the use of conditional performance measures that focus on rare events only in addition to standardly used unconditional indicators. The findings of the study directly address road and traffic management but can be transferred to a range of other environmental variables including meteorological and hydrological quantities.

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Section: Threshold Excess Methodsmentioning

confidence: 99%

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Schlögl

Laaha

2017

Nat. Hazards Earth Syst. Sci.

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“…This resolves the intrinsic problem of threshold stability of the GPD in the nonstationary case (cf. Eastoe & Tawn, 2009;Northrop, Jonathan, & Randell, 2016); to the best of our knowledge, such a solution is new. Due to analytical and computational complexities, estimation of the model parameters and variable selection in both Models I and II were carried out within the Bayesian framework by using a suitable Markov chain Monte Carlo (MCMC) procedure (Gilks, Richardson, & Spiegelhalter, 1996).…”

Section: Peaks-over-threshold Modelsmentioning

confidence: 99%

“…In the presence of nonstationarity, the use of such diagnostic tools is not fully justified and may be questionable. As an alternative, more sophisticated threshold choice procedures are available in the nonstationary context; for example, Northrop and Jonathan (2011) proposed a method for setting covariate-dependent thresholds using quantile regression, whereas Northrop et al (2016) focused on graphical methods for choosing time-dependent thresholds. Such methods are not used here because our primary aim is to model the exceedances of fixed thresholds, which in practice may be directly associated with the air quality standards or critical medical levels.…”

Section: Threshold Selectionmentioning

confidence: 99%

Nonstationary POT modelling of air pollution concentrations: Statistical analysis of the traffic and meteorological impact

2017

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Predicting the occurrence, level and duration of high air pollution concentrations exceeding a given critical level enables researchers to study the health impact of road traffic on local air quality and to inform public policy action. Precise estimates of the probabilities of occurrence and level of extreme concentrations are formidable due to the combination of complex physical and chemical processes involved. This underpins the need for developing sophisticated extreme value models, in particular allowing for non-stationarity of environmental time series. In this paper, extremes of nitrogen oxide (NO), nitrogen dioxide (NO 2 ) and ozone (O 3 ) concentrations are investigated using two models. Model I is based on an extended peaks-over-threshold (POT) approach developed by A. C. Davison and R. L. Smith, whereby the parameters of the underlying generalized Pareto distribution (GPD) are treated as functions of covariates (i.e., traffic and meteorological factors). The new Model II resolves the lack of threshold stability in the Davison-Smith model by constructing a special functional form for the GPD parameters. For each of the models, the effects of traffic and meteorological factors on the frequency and size of extreme values are estimated using Markov chain Monte Carlo methods. Finally, appropriate goodness-of-fit tests and model selection criteria confirm that Model II significantly outperforms Model I in estimation and forecasting of extremes.

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“…This assessment is largely subjective. Northrop and Coleman [38] and Wadsworth [39] reduce this subjectivity using a likelihood-based procedure to produce complementary plots that enable an automated threshold selection. Figure 4 shows the daily flow time series against series at Lag 1 for the three stations, and the red lines in the plots represent the thresholds.…”

Section: Threshold Selection and Pot Seriesmentioning

confidence: 99%

Frequency Analysis of High Flow Extremes in the Yingluoxia Watershed in Northwest China

Wang

Zhao

et al. 2016

Water

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Statistical modeling of hydrological extremes is significant to the construction of hydraulic engineering. This paper, taking the Yingluoxia watershed as the study area, compares the annual maximum (AM) series and the peaks over a threshold (POT) series in order to study the hydrological extremes, examines the stationarity and independence assumptions for the two series, and discusses the estimations and uncertainties of return levels from the two series using the Generalized Extreme Value (GEV) and Generalized Pareto distribution (GPD) models. For comparison, the return levels from all threshold excesses with considering the extremal index are also estimated. For the POT series, the threshold is selected by examining the mean excess plot and the stability of the parameter estimates and by using common-sense. The serial correlation is reduced by filtering out a set of dependent threshold excesses. Results show that both series are approximately stationary and independent. The GEV model fits the AM series well and the GPD model fits the POT series well. The estimated return levels are fairly comparable for the AM series, the POT series, and all threshold excesses with considering the extremal index, with the difference being less than 10% for return periods longer than 10 years. The uncertainties of the estimated return levels are the highest for the AM series, and next for the POT series and then for all threshold excesses series in turn.

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Improved threshold diagnostic plots for extreme value analyses

Cited by 45 publications

References 11 publications

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Extreme weather exposure identification for road networks – a comparative assessment of statistical methods

Nonstationary POT modelling of air pollution concentrations: Statistical analysis of the traffic and meteorological impact

Frequency Analysis of High Flow Extremes in the Yingluoxia Watershed in Northwest China

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