اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDirectional Multivariate Extremes in Environmental Phenomena
280
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Several environmental phenomena can be described by different correlated variables that must be considered jointly in order to be more representative of the nature of these phenomena. For such events, identification of extremes is inappropriate if it is based on marginal analysis. Extremes have usually been linked to the notion of quantile, which is an important tool to analyze risk in the univariate setting. We propose to identify multivariate extremes and analyze environmental phenomena in terms of the directional multivariate quantile, which allows us to analyze the data considering all the variables implied in the phenomena, as well as look at the data in interesting directions that can better describe an environmental catastrophe. Since there are many references in the literature that propose extremes detection based on copula models, we also generalize the copula method by introducing the directional approach. Advantages and disadvantages of the non-parametric proposal that we introduce and the copula methods are provided in the paper. We show with simulated and real data sets how by considering the first principal component direction we can improve the visualization of extremes. Finally, two cases of study are analyzed: a synthetic case of flood risk at a dam (a 3-variable case), and a real case study of sea storms (a 5-variable case).
قيم البحث
اقرأ أيضاً
In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into t
he MEVT, giving the opportunity to characterize the recently introduced directional multivariate quantiles (DMQ) at high levels. Then, an out-sample estimation method for these quantiles is given. A bootstrap procedure carries out the estimation of the tuning parameter in this multivariate framework and helps with the estimation of the DMQ. Asymptotic normality for the proposed estimator is provided and the methodology is illustrated with simulated data-sets. Finally, a real-life application to a financial case is also performed.
Severe thunderstorms can have devastating impacts. Concurrently high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are known to be conducive to severe weather, so high values of PROD=$sqrt{mathrm{CAPE}} time
s$SRH have been used to indicate high risk of severe thunderstorms. We consider the extreme values of these three variables for a large area of the contiguous US over the period 1979-2015, and use extreme-value theory and a multiple testing procedure to show that there is a significant time trend in the extremes for PROD maxima in April, May and August, for CAPE maxima in April, May and June, and for maxima of SRH in April and May. These observed increases in CAPE are also relevant for rainfall extremes and are expected in a warmer climate, but have not previously been reported. Moreover, we show that the El Ni~no-Southern Oscillation explains variation in the extremes of PROD and SRH in February. Our results suggest that the risk from severe thunderstorms in April and May is increasing in parts of the US where it was already high, and that the risk from storms in February tends to be higher over the main part of the region during La Ni~na years. Our results differ from those obtained in earlier studies using extreme-value techniques to analyze a quantity similar to PROD.
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $alpha$, the $100alpha%$ VaR is defined as a thres
hold loss value, such that the probability that the loss on the portfolio over the given time horizon exceeds this value is $alpha$. That is to say, it is a quantile of the distribution of the losses, which has both good analytic properties and easy interpretation as a risk measure. However, its extension to the multivariate framework is not unique because a unique definition of multivariate quantile does not exist. In the current literature, the multivariate quantiles are related to a specific partial order considered in $mathbb{R}^{n}$, or to a property of the univariate quantile that is desirable to be extended to $mathbb{R}^{n}$. In this work, we introduce a multivariate value at risk as a vector-valued directional risk measure, based on a directional multivariate quantile, which has recently been introduced in the literature. The directional approach allows the manager to consider external information or risk preferences in her/his analysis. We have derived some properties of the risk measure and we have compared the univariate textit{VaR} over the marginals with the components of the directional multivariate VaR. We have also analyzed the relationship between some families of copulas, for which it is possible to obtain closed forms of the multivariate VaR that we propose. Finally, comparisons with other alternative multivariate VaR given in the literature, are provided in terms of robustness.
The gridding of daily accumulated precipitation -- especially extremes -- from ground-based station observations is problematic due to the fractal nature of precipitation, and therefore estimates of long period return values and their changes based o
n such gridded daily data sets are generally underestimated. In this paper, we characterize high-resolution changes in observed extreme precipitation from 1950 to 2017 for the contiguous United States (CONUS) based on in situ measurements only. Our analysis utilizes spatial statistical methods that allow us to derive gridded estimates that do not smooth extreme daily measurements and are consistent with statistics from the original station data while increasing the resulting signal to noise ratio. Furthermore, we use a robust statistical technique to identify significant pointwise changes in the climatology of extreme precipitation while carefully controlling the rate of false positives. We present and discuss seasonal changes in the statistics of extreme precipitation: the largest and most spatially-coherent pointwise changes are in fall (SON), with approximately 33% of CONUS exhibiting significant changes (in an absolute sense). Other seasons display very few meaningful pointwise changes (in either a relative or absolute sense), illustrating the difficulty in detecting pointwise changes in extreme precipitation based on in situ measurements. While our main result involves seasonal changes, we also present and discuss annual changes in the statistics of extreme precipitation. In this paper we only seek to detect changes over time and leave attribution of the underlying causes of these changes for future work.
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an asymptotic distrib
ution as the proper fit to observations from the tail. This paper provides a holistic approach to the modelling of non-stationary extreme events by iterating between parametric and semi-parametric approaches, thus providing an automatic procedure to estimate a moving threshold with respect to a periodic covariate in circular data. By exploiting advantages and mitigating pitfalls of each approach, a unified framework is provided as the backbone for estimating extreme quantiles, including that of the $T$-year level and finite right endpoint, which seeks to optimize bias-variance trade-off. To this end, two tuning parameters related to the spread of peaks over threshold are introduced. We provide guidance for applying the methodology to the directional modelling of hindcast storm peak significant wave heights recorded in the North Sea. Although the theoretical underpinning for adaptation of well-known estimators in statistics of extremes to circular data is given in some detail, the derivation of their asymptotic properties lays beyond the scope of this paper. A bootstrap technique is implemented for obtaining direction-driven confidence bounds in such a way as to account for the relevant boundary restrictions with minimal sensitivity to initial point. This provides a template for other applications where the analysis of directional extremes is of importance.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
