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Artículos de revistas sobre el tema "Extreme quantile estimation"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 2 de febrero de 2022

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1

Li, Deyuan, and Huixia Judy Wang. "Extreme Quantile Estimation for Autoregressive Models." Journal of Business & Economic Statistics 37, no. 4 (2018): 661–70. http://dx.doi.org/10.1080/07350015.2017.1408469.

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2

CAI, YUZHI. "A COMPARATIVE STUDY OF MONOTONE QUANTILE REGRESSION METHODS FOR FINANCIAL RETURNS." International Journal of Theoretical and Applied Finance 19, no. 03 (2016): 1650016. http://dx.doi.org/10.1142/s0219024916500163.

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Quantile regression methods have been used widely in finance to alleviate estimation problems related to the impact of outliers and the fat-tailed error distribution of financial returns. However, a potential problem with the conventional quantile regression method is that the estimated conditional quantiles may cross over, leading to a failure of the analysis. It is noticed that the crossing over issues usually occur at high or low quantile levels, which are the quantile levels of great interest when analyzing financial returns. Several methods have appeared in the literature to tackle this problem. This study compares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, for estimating noncrossing conditional quantiles by using four financial return series. We found that all these methods provide similar quantiles at nonextreme quantile levels. However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilers may underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai & Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methods provide similar median forecasts.

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3

Kithinji, Martin M., Peter N. Mwita, and Ananda O. Kube. "Adjusted Extreme Conditional Quantile Autoregression with Application to Risk Measurement." Journal of Probability and Statistics 2021 (April 7, 2021): 1–10. http://dx.doi.org/10.1155/2021/6697120.

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In this paper, we propose an extreme conditional quantile estimator. Derivation of the estimator is based on extreme quantile autoregression. A noncrossing restriction is added during estimation to avert possible quantile crossing. Consistency of the estimator is derived, and simulation results to support its validity are also presented. Using Average Root Mean Squared Error (ARMSE), we compare the performance of our estimator with the performances of two existing extreme conditional quantile estimators. Backtest results of the one-day-ahead conditional Value at Risk forecasts are also given.

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4

He, Yi, and John H. J. Einmahl. "Estimation of extreme depth-based quantile regions." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79, no. 2 (2016): 449–61. http://dx.doi.org/10.1111/rssb.12163.

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5

Gardes, Laurent. "Tail dimension reduction for extreme quantile estimation." Extremes 21, no. 1 (2017): 57–95. http://dx.doi.org/10.1007/s10687-017-0300-x.

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6

Onyutha, Charles, and Patrick Willems. "Uncertainty in calibrating generalised Pareto distribution to rainfall extremes in Lake Victoria basin." Hydrology Research 46, no. 3 (2014): 356–76. http://dx.doi.org/10.2166/nh.2014.052.

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Uncertainty in the calibration of the generalised Pareto distribution (GPD) to rainfall extremes is assessed based on observed and large number of global climate model rainfall time series for nine locations in the Lake Victoria basin (LVB) in Eastern Africa. The class of the GPD suitable for capturing the tail behaviour of the distribution and extreme quantiles is investigated. The best parameter estimation method is selected following comparison of the method of moments, maximum likelihood, L-moments, and weighted linear regression in quantile plots (WLR) to quantify uncertainty in the extreme intensity quantiles by employing the Jackknife method and nonparametric percentile bootstrapping in a combined way. The normal tailed GPD was found suitable. Although the performance of each parameter estimation method was acceptable in a number of evaluation criteria, generally the WLR technique appears to be more robust than others. The difference between upper and lower limits of the 95% confidence intervals expressed as a percentage of the empirical 10-year rainfall intensity quantile ranges from 9.25 up to 59.66%. The assessed uncertainty will be useful in support of risk based planning, design and operation of water engineering and water management applications related to floods in the LVB.

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7

You, Alexandre, Ulrike Schneider, Armelle Guillou, and Philippe Naveau. "Improving extreme quantile estimation via a folding procedure." Journal of Statistical Planning and Inference 140, no. 7 (2010): 1775–87. http://dx.doi.org/10.1016/j.jspi.2010.01.007.

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8

Morio, Jérôme. "Extreme quantile estimation with nonparametric adaptive importance sampling." Simulation Modelling Practice and Theory 27 (September 2012): 76–89. http://dx.doi.org/10.1016/j.simpat.2012.05.008.

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9

Kim, Sojung, Kyoung-Kuk Kim, and Heelang Ryu. "Robust quantile estimation under bivariate extreme value models." Extremes 23, no. 1 (2019): 55–83. http://dx.doi.org/10.1007/s10687-019-00362-2.

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10

Dutta, Santanu, and Suparna Biswas. "Extreme quantile estimation based on financial time series." Communications in Statistics - Simulation and Computation 46, no. 6 (2017): 4226–43. http://dx.doi.org/10.1080/03610918.2015.1112908.

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11

Lebrenz, Henning, and András Bárdossy. "Geostatistical interpolation by quantile kriging." Hydrology and Earth System Sciences 23, no. 3 (2019): 1633–48. http://dx.doi.org/10.5194/hess-23-1633-2019.

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Abstract. The widely applied geostatistical interpolation methods of ordinary kriging (OK) or external drift kriging (EDK) interpolate the variable of interest to the unknown location, providing a linear estimator and an estimation variance as measure of uncertainty. The methods implicitly pose the assumption of Gaussianity on the observations, which is not given for many variables. The resulting “best linear and unbiased estimator” from the subsequent interpolation optimizes the mean error over many realizations for the entire spatial domain and, therefore, allows a systematic under-(over-)estimation of the variable in regions of relatively high (low) observations. In case of a variable with observed time series, the spatial marginal distributions are estimated separately for one time step after the other, and the errors from the interpolations might accumulate over time in regions of relatively extreme observations. Therefore, we propose the interpolation method of quantile kriging (QK) with a two-step procedure prior to interpolation: we firstly estimate distributions of the variable over time at the observation locations and then estimate the marginal distributions over space for every given time step. For this purpose, a distribution function is selected and fitted to the observed time series at every observation location, thus converting the variable into quantiles and defining parameters. At a given time step, the quantiles from all observation locations are then transformed into a Gaussian-distributed variable by a 2-fold quantile–quantile transformation with the beta- and normal-distribution function. The spatio-temporal description of the proposed method accommodates skewed marginal distributions and resolves the spatial non-stationarity of the original variable. The Gaussian-distributed variable and the distribution parameters are now interpolated by OK and EDK. At the unknown location, the resulting outcomes are reconverted back into the estimator and the estimation variance of the original variable. As a summary, QK newly incorporates information from the temporal axis for its spatial marginal distribution and subsequent interpolation and, therefore, could be interpreted as a space–time version of probability kriging. In this study, QK is applied for the variable of observed monthly precipitation from raingauges in South Africa. The estimators and estimation variances from the interpolation are compared to the respective outcomes from OK and EDK. The cross-validations show that QK improves the estimator and the estimation variance for most of the selected objective functions. QK further enables the reduction of the temporal bias at locations of extreme observations. The performance of QK, however, declines when many zero-value observations are present in the input data. It is further revealed that QK relates the magnitude of its estimator with the magnitude of the respective estimation variance as opposed to the traditional methods of OK and EDK, whose estimation variances do only depend on the spatial configuration of the observation locations and the model settings.

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12

Chavez-Demoulin, Valérie, та Armelle Guillou. "Extreme quantile estimation forβ-mixing time series and applications". Insurance: Mathematics and Economics 83 (листопад 2018): 59–74. http://dx.doi.org/10.1016/j.insmatheco.2018.09.004.

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13

Dekkers, Arnold L. M., and Laurens De Haan. "On the Estimation of the Extreme-Value Index and Large Quantile Estimation." Annals of Statistics 17, no. 4 (1989): 1795–832. http://dx.doi.org/10.1214/aos/1176347396.

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14

Beirlant, J., G. Dierckx, and A. Guillou. "Estimation of the extreme-value index and generalized quantile plots." Bernoulli 11, no. 6 (2005): 949–70. http://dx.doi.org/10.3150/bj/1137421635.

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15

Ferreira, Ana. "Spatial aggregation and high quantile estimation applied to extreme precipitation." Statistics and Its Interface 8, no. 1 (2015): 33–43. http://dx.doi.org/10.4310/sii.2015.v8.n1.a4.

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16

Drees, Holger. "Extreme quantile estimation for dependent data, with applications to finance." Bernoulli 9, no. 4 (2003): 617–57. http://dx.doi.org/10.3150/bj/1066223272.

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17

Yun, Seok-Hoon. "Extreme Quantile Estimation of Losses in KRW/USD Exchange Rate." Communications for Statistical Applications and Methods 16, no. 5 (2009): 803–12. http://dx.doi.org/10.5351/ckss.2009.16.5.803.

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18

Castillo, Enrique, and Ali S. Hadi. "Parameter and quantile estimation for the generalized extreme-value distribution." Environmetrics 5, no. 4 (1994): 417–32. http://dx.doi.org/10.1002/env.3170050405.

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19

Falk, Michael. "Extreme quantile estimation in δ-neighborhoods of generalized Pareto distributions". Statistics & Probability Letters 20, № 1 (1994): 9–21. http://dx.doi.org/10.1016/0167-7152(94)90229-1.

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20

Sigauke, Caston, Andréhette Verster, and Delson Chikobvu. "Extreme daily increases in peak electricity demand: Tail-quantile estimation." Energy Policy 53 (February 2013): 90–96. http://dx.doi.org/10.1016/j.enpol.2012.10.073.

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21

Beranger, Boris, Simone A. Padoan, and Scott A. Sisson. "Correction to: Estimation and uncertainty quantification for extreme quantile regions." Extremes 24, no. 2 (2021): 377–78. http://dx.doi.org/10.1007/s10687-021-00408-4.

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22

Degen, Matthias, and Paul Embrechts. "Scaling of High-Quantile Estimators." Journal of Applied Probability 48, no. 04 (2011): 968–83. http://dx.doi.org/10.1017/s0021900200008561.

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Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

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23

Degen, Matthias, and Paul Embrechts. "Scaling of High-Quantile Estimators." Journal of Applied Probability 48, no. 4 (2011): 968–83. http://dx.doi.org/10.1239/jap/1324046013.

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Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

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24

Gerke, Oke. "Nonparametric Limits of Agreement in Method Comparison Studies: A Simulation Study on Extreme Quantile Estimation." International Journal of Environmental Research and Public Health 17, no. 22 (2020): 8330. http://dx.doi.org/10.3390/ijerph17228330.

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Bland–Altman limits of agreement and the underlying plot are a well-established means in method comparison studies on quantitative outcomes. Normally distributed paired differences, a constant bias, and variance homogeneity across the measurement range are implicit assumptions to this end. Whenever these assumptions are not fully met and cannot be remedied by an appropriate transformation of the data or the application of a regression approach, the 2.5% and 97.5% quantiles of the differences have to be estimated nonparametrically. Earlier, a simple Sample Quantile (SQ) estimator (a weighted average of the observations closest to the target quantile), the Harrell–Davis estimator (HD), and estimators of the Sfakianakis–Verginis type (SV) outperformed 10 other quantile estimators in terms of mean coverage for the next observation in a simulation study, based on sample sizes between 30 and 150. Here, we investigate the variability of the coverage probability of these three and another three promising nonparametric quantile estimators with n=50(50)200,250(250)1000. The SQ estimator outperformed the HD and SV estimators for n=50 and was slightly better for n=100, whereas the SQ, HD, and SV estimators performed identically well for n≥150. The similarity of the boxplots for the SQ estimator across both distributions and sample sizes was striking.

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25

Pandey, M. D. "Extreme quantile estimation using order statistics with minimum cross-entropy principle." Probabilistic Engineering Mechanics 16, no. 1 (2001): 31–42. http://dx.doi.org/10.1016/s0266-8920(00)00004-7.

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26

Kim, Joonpyo, Seoncheol Park, Junhyeon Kwon, Yaeji Lim, and Hee-Seok Oh. "Estimation of spatio-temporal extreme distribution using a quantile factor model." Extremes 24, no. 1 (2021): 177–95. http://dx.doi.org/10.1007/s10687-020-00404-0.

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27

Kithinji, Martin M., Peter N. Mwita, and Ananda O. Kube. "Estimation of Conditional Weighted Expected Shortfall under Adjusted Extreme Quantile Autoregression." Journal of Mathematical Finance 11, no. 03 (2021): 373–85. http://dx.doi.org/10.4236/jmf.2021.113021.

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28

Wu, Jiannan. "Estimating models of extreme behavior: A Monte Carlo comparison between SWAT and Quantile regression." Chinese Public Administration Review 1, no. 2 (2006): 165. http://dx.doi.org/10.22140/cpar.v1i2.21.

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We are interested in theoretical explanations of extreme behavior in social and management science situations. For example, in studying organizational performance we theorize that organzations achieve high levels of performance by employing innovative or unique behavioral characteristics. Methodologically, several approaches that provdie tools for modeling extreme behavior: substantively weighted analytical techniques (SWAR) and quantile regression. We evaluate both for their ability to accurately estimate models of extreme behavior when that behavior significantly differs from the average case. Since we attempt to evaluate statistical approaches in situations where standard axiomatic approaches fall short, our strategiy is to use simulation techniques where the underlying data-generating structure is knows and designed to have different underlying mathematical relationships between the middle and the two extremes. We also apply a Monte Carlo approach of repeated simulations to investigate the sampling characteristics of these apporoaches. Finally, we apply standard measure for evaulation of statistical estimators, mean square error, to examine both the bias and the relative efficiency of each approach. The experimental results demonstrate that quantile regression provides a more accurate and reliable estimation of extreme pheneomena.

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29

Beneyto, Carles, José Ángel Aranda, Gerardo Benito, and Félix Francés. "New Approach to Estimate Extreme Flooding Using Continuous Synthetic Simulation Supported by Regional Precipitation and Non-Systematic Flood Data." Water 12, no. 11 (2020): 3174. http://dx.doi.org/10.3390/w12113174.

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Stochastic weather generators combined with hydrological models have been proposed for continuous synthetic simulation to estimate return periods of extreme floods. Yet, this approach relies upon the length and spatial distribution of the precipitation input data series, which often are scarce, especially in arid and semiarid regions. In this work, we present a new approach for the estimation of extreme floods based on the continuous synthetic simulation method supported with inputs of (a) a regional study of extreme precipitation to improve the calibration of the weather generator (GWEX), and (b) non-systematic flood information (i.e., historical information and/or palaeoflood records) for the validation of the generated discharges with a fully distributed hydrological model (TETIS). The results showed that this complementary information of extremes allowed for a more accurate implementation of both the weather generator and the hydrological model. This, in turn, improved the flood quantile estimates, especially for those associated with return periods higher than 50 years but also for higher quantiles (up to approximately 500 years). Therefore, it has been proved that continuous synthetic simulation studies focused on the estimation of extreme floods should incorporate a generalized representation of regional extreme rainfall and/or non-systematic flood data, particularly in regions with scarce hydrometeorological records.

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30

Hu, Yi-Ming, Zhong-Min Liang, Bin-Quan Li, and Zhong-Bo Yu. "Uncertainty Assessment of Hydrological Frequency Analysis Using Bootstrap Method." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/724632.

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The hydrological frequency analysis (HFA) is the foundation for the hydraulic engineering design and water resources management. Hydrological extreme observations or samples are the basis for HFA; the representativeness of a sample series to the population distribution is extremely important for the estimation reliability of the hydrological design value or quantile. However, for most of hydrological extreme data obtained in practical application, the size of the samples is usually small, for example, in China about 40~50 years. Generally, samples with small size cannot completely display the statistical properties of the population distribution, thus leading to uncertainties in the estimation of hydrological design values. In this paper, a new method based on bootstrap is put forward to analyze the impact of sampling uncertainty on the design value. By bootstrap resampling technique, a large number of bootstrap samples are constructed from the original flood extreme observations; the corresponding design value or quantile is estimated for each bootstrap sample, so that the sampling distribution of design value is constructed; based on the sampling distribution, the uncertainty of quantile estimation can be quantified. Compared with the conventional approach, this method provides not only the point estimation of a design value but also quantitative evaluation on uncertainties of the estimation.

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31

Bolancé, Catalina, and Carlos Alberto Acuña. "A New Kernel Estimator of Copulas Based on Beta Quantile Transformations." Mathematics 9, no. 10 (2021): 1078. http://dx.doi.org/10.3390/math9101078.

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A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0,1). For this reason, a classical kernel estimator does not work and this estimator needs to be corrected at boundaries, which increases the difficulty of the estimation and, in practice, the bias boundary correction might not provide the desired improvement. A quantile transformation of marginals is a way to improve the classical kernel approach. This paper shows a Beta quantile transformation to be optimal and analyses a kernel estimator based on this transformation. Furthermore, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves alternative kernel estimators of copulas. We illustrate our proposal with a financial risk data analysis.

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32

Fischer, S., R. Fried, and A. Schumann. "Examination for robustness of parametric estimators for flood statistics in the context of extraordinary extreme events." Hydrology and Earth System Sciences Discussions 12, no. 8 (2015): 8553–76. http://dx.doi.org/10.5194/hessd-12-8553-2015.

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Abstract. We compare several estimators, which are commonly used in hydrology, for the parameters of the distribution of flood series, like the Maximum-Likelihood estimator or L-Moments, with the robust estimators Trimmed L-Moments and Minimum Distances. Our objective is estimation of the 99 %- or 99.9 %-quantile of an underlying Gumbel or Generalized Extreme Value distribution (GEV), where we modify the generated random variables such that extraordinary extreme events occur. The results for a two- or three-parametric fitting are compared and the robustness of the estimators to the occurrence of extraordinary extreme events is investigated by statistical measures. When extraordinary extreme events are known to appear in the sample, the Trimmed L-Moments are a recommendable choice for a robust estimation. They even perform rather well, if there are no such events.

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33

Ho, Kwok-Wah. "A matching prior for extreme quantile estimation of the generalized Pareto distribution." Journal of Statistical Planning and Inference 140, no. 6 (2010): 1513–18. http://dx.doi.org/10.1016/j.jspi.2009.12.012.

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34

Jesus, Lucas Filipe Lucena, Veber Costa, and Wilson Fernandes. "Evaluating the influence of extending hydrologic time series in extreme quantile estimation." Water and Environment Journal 34, S1 (2020): 804–19. http://dx.doi.org/10.1111/wej.12579.

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35

Rutikanga, Justin Ushize, and Aliou Diop. "Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring." Open Journal of Statistics 11, no. 01 (2021): 162–77. http://dx.doi.org/10.4236/ojs.2021.111009.

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36

Cerović, Julija, Milena Lipovina-Božović, and Saša Vujošević. "A Comparative Analysis of Value at Risk Measurement on Emerging Stock Markets: Case of Montenegro." Business Systems Research Journal 6, no. 1 (2015): 36–55. http://dx.doi.org/10.1515/bsrj-2015-0003.

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Abstract Background: The concept of value at risk gives estimation of the maximum loss of financial position at a given time for a given probability. The motivation for this analysis lies in the desire to devote necessary attention to risks in Montenegro, and to approach to quantifying and managing risk more thoroughly. Objectives: This paper considers adequacy of the most recent approaches for quantifying market risk, especially of methods that are in the basis of extreme value theory, in Montenegrin emerging market before and during the global financial crisis. In particular, the purpose of the paper is to investigate whether extreme value theory outperforms econometric and quantile evaluation of VaR in emerging stock markets such as Montenegrin market. Methods/Approach: Daily return of Montenegrin stock market index MONEX20 is analyzed for the period January, 2004 - February, 2014. Value at Risk results based on GARCH models, quantile estimation and extreme value theory are compared. Results: Results of the empirical analysis show that the assessments of Value at Risk based on extreme value theory outperform econometric and quantile evaluations. Conclusions: It is obvious that econometric evaluations (ARMA(2,0)- GARCH(1,1) and RiskMetrics) proved to be on the lower bound of possible Value at Risk movements. Risk estimation on emerging markets can be focused on methodology using extreme value theory that is more sophisticated as it has been proven to be the most cautious model when dealing with turbulent times and financial turmoil.

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37

Shao, Yuehong, Jun Zhao, Jinchao Xu, Aolin Fu, and Junmei Wu. "Revision of Frequency Estimates of Extreme Precipitation Based on the Annual Maximum Series in the Jiangsu Province in China." Water 13, no. 13 (2021): 1832. http://dx.doi.org/10.3390/w13131832.

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Frequency estimates of extreme precipitation are revised using a regional L-moments method based on the annual maximum series and Chow’s equation at lower return periods for the Jiangsu area in China. First, the study area is divided into five homogeneous regions, and the optimum distribution for each region is determined by an integrative assessment. Second, underestimation of quantiles and the applicability of Chow’s equation are verified. The results show that quantiles are underestimated based on the annual maximum series, and that Chow’s formula is applicable for the study area. Next, two methods are used to correct the underestimation of frequency estimation. A set of rational and reliable frequency estimations is obtained using the regional L-moments method and the two revised methods, which can indirectly provide a robust basis for flood control and water resource management. This study extends previous works by verifying underestimation of the quantiles and the provision of two improved methods for obtaining reliable quantile estimations of extreme precipitation at lower recurrence intervals, especially in solving reliable estimates for a 1-year return period from the integral lower limit of the frequency distribution.

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38

Elsinghorst, C., P. Groeneboom, P. Jonathan, L. Smulders, and P. H. Taylor. "Extreme Value Analysis of North Sea Storm Severity." Journal of Offshore Mechanics and Arctic Engineering 120, no. 3 (1998): 177–83. http://dx.doi.org/10.1115/1.2829538.

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In this paper we consider the estimation of North Sea storm severity, for storms with return periods in the interval 100 to 500 yr. The analysis consists of: modeling the tail-distribution for a set of data for storm severity (using, e.g., storm hindcast data); estimating extreme storm severity; estimating confidence intervals for extreme storm severity; validating the bias and variance of estimates using simulation studies, for known underlying model forms; and estimating the robustness of extreme quantile estimates with respect to misspecification of the underlying model for the tail-distribution of storm severity. Applications to NESS (Northern European Hindcast Study) hindcast data at clusters of locations in the northern, central and southern North Sea are considered. Results suggest, in particular, the existence of a physical upper limit for storm severity in the North Sea and a close to constant value for the extreme value index, γ ≈ −0.2.

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39

Brazauskas, Vytaras, and Sahadeb Upretee. "Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions." Risks 7, no. 2 (2019): 55. http://dx.doi.org/10.3390/risks7020055.

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Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as in pricing of extreme events, developing reserve estimates, designing risk transfer strategies, and allocating capital. In this paper, we present the empirical nonparametric and two types of parametric estimators of quantiles at various levels. For parametric estimation, we employ the maximum likelihood and percentile-matching approaches. Asymptotic distributions of all the estimators under consideration are derived when data are left-truncated and right-censored, which is a typical loss variable modification in insurance. Then, we construct relative efficiency curves (REC) for all the parametric estimators. Specific examples of such curves are provided for exponential and single-parameter Pareto distributions for a few data truncation and censoring cases. Additionally, using simulated data we examine how wrong quantile estimates can be when one makes incorrect modeling assumptions. The numerical analysis is also supplemented with standard model diagnostics and validation (e.g., quantile-quantile plots, goodness-of-fit tests, information criteria) and presents an example of when those methods can mislead the decision maker. These findings pave the way for further work on RECs with potential for them being developed into an effective diagnostic tool in this context.

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40

Ferrari, Davide, and Sandra Paterlini. "The Maximum Lq-Likelihood Method: An Application to Extreme Quantile Estimation in Finance." Methodology and Computing in Applied Probability 11, no. 1 (2008): 3–19. http://dx.doi.org/10.1007/s11009-007-9063-1.

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41

Pan, Qiyun, Eunshin Byon, Young Myoung Ko, and Henry Lam. "Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models." Naval Research Logistics (NRL) 67, no. 7 (2020): 524–47. http://dx.doi.org/10.1002/nav.21938.

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42

Dupuis, D. J. "Parameter and quantile estimation for the generalized extreme-value distribution: a second look." Environmetrics 10, no. 1 (1999): 119–24. http://dx.doi.org/10.1002/(sici)1099-095x(199901/02)10:1<119::aid-env342>3.0.co;2-s.

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43

Yi, Yanping, Xingdong Feng, and Zhuo Huang. "Estimation of extreme value-at-risk: An EVT approach for quantile GARCH model." Economics Letters 124, no. 3 (2014): 378–81. http://dx.doi.org/10.1016/j.econlet.2014.06.028.

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44

Hu, Jie, Yu Chen, and Keqi Tan. "ESTIMATION OF HIGH CONDITIONAL TAIL RISK BASED ON EXPECTILE REGRESSION." ASTIN Bulletin 51, no. 2 (2021): 539–70. http://dx.doi.org/10.1017/asb.2021.3.

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Resumen

AbstractAssessing conditional tail risk at very high or low levels is of great interest in numerous applications. Due to data sparsity in high tails, the widely used quantile regression method can suffer from high variability at the tails, especially for heavy-tailed distributions. As an alternative to quantile regression, expectile regression, which relies on the minimization of the asymmetric l2-norm and is more sensitive to the magnitudes of extreme losses than quantile regression, is considered. In this article, we develop a new estimation method for high conditional tail risk by first estimating the intermediate conditional expectiles in regression framework, and then estimating the underlying tail index via weighted combinations of the top order conditional expectiles. The resulting conditional tail index estimators are then used as the basis for extrapolating these intermediate conditional expectiles to high tails based on reasonable assumptions on tail behaviors. Finally, we use these high conditional tail expectiles to estimate alternative risk measures such as the Value at Risk (VaR) and Expected Shortfall (ES), both in high tails. The asymptotic properties of the proposed estimators are investigated. Simulation studies and real data analysis show that the proposed method outperforms alternative approaches.

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45

Frau, Roberto, Marc Andreewsky, and Pietro Bernardara. "The use of historical information for regional frequency analysis of extreme skew surge." Natural Hazards and Earth System Sciences 18, no. 3 (2018): 949–62. http://dx.doi.org/10.5194/nhess-18-949-2018.

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Abstract. The design of effective coastal protections requires an adequate estimation of the annual occurrence probability of rare events associated with a return period up to 103 years. Regional frequency analysis (RFA) has been proven to be an applicable way to estimate extreme events by sorting regional data into large and spatially distributed datasets. Nowadays, historical data are available to provide new insight on past event estimation. The utilisation of historical information would increase the precision and the reliability of regional extreme's quantile estimation. However, historical data are from significant extreme events that are not recorded by tide gauge. They usually look like isolated data and they are different from continuous data from systematic measurements of tide gauges. This makes the definition of the duration of our observations period complicated. However, the duration of the observation period is crucial for the frequency estimation of extreme occurrences. For this reason, we introduced here the concept of “credible duration”. The proposed RFA method (hereinafter referenced as FAB, from the name of the authors) allows the use of historical data together with systematic data, which is a result of the use of the credible duration concept.

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46

Park, Jeong-Soo. "A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution." Mathematics and Computers in Simulation 70, no. 4 (2005): 227–34. http://dx.doi.org/10.1016/j.matcom.2005.09.003.

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47

Diebolt, Jean, and Stéphane Girard. "A note on the asymptotic normality of the ET method for extreme quantile estimation." Statistics & Probability Letters 62, no. 4 (2003): 397–405. http://dx.doi.org/10.1016/s0167-7152(03)00045-2.

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48

Muraleedharan, G., Cláudia Lucas, C. Guedes Soares, N. Unnikrishnan Nair, and P. G. Kurup. "Modelling significant wave height distributions with quantile functions for estimation of extreme wave heights." Ocean Engineering 54 (November 2012): 119–31. http://dx.doi.org/10.1016/j.oceaneng.2012.07.007.

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49

BARDSLEY, W. E., and C. P. PEARSON. "An experiment in subjective graphical quantile estimation applied to the generalized extreme value distribution." Hydrological Sciences Journal 44, no. 3 (1999): 399–405. http://dx.doi.org/10.1080/02626669909492235.

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50

Matulessy, Esther Ria, Aji Hamim Wigena, and Anik Djuraidah. "Quantile regression with partial least squares in statistical downscaling for estimation of extreme rainfall." Applied Mathematical Sciences 9 (2015): 4489–98. http://dx.doi.org/10.12988/ams.2015.53254.

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