Explore the vast range of titles available.

Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used for extrapolation beyond the range of observed values and estimation of conditional extreme quantiles. Based on the peaks-over-threshold approach, the conditional distribution above a high threshold is approximated by a generalized Pareto distribution with covariate dependent parameters. We propose a gradient boosting procedure to estimate a conditional generalized Pareto distribution by minimizing its deviance. Cross-validation is used for the choice of tuning parameters such as the number of trees and the tree depths. We discuss diagnostic plots such as variable importance and partial dependence plots, which help to interpret the fitted models. In simulation studies we show that our gradient boosting procedure outperforms classical methods from quantile regression and extreme value theory, especially for high-dimensional predictor spaces and complex parameter response surfaces. An application to statistical post-processing of weather forecasts with precipitation data in the Netherlands is proposed.

This article develops a threshold system for monitoring airline performance. This threshold system divides the sample space into regions with increasing levels of risk and allows instant assessments of risk level of any observed airline performance. Of particular concern is the performance with extreme risk. In this article, a multivariate extreme value theory approach is used to establish thresholds for signaling varying levels of extremeness in the context of simultaneous monitoring of multiple risk measures. The threshold system is justified in terms of multivariate extreme quantiles, and its sample estimator is shown to be consistent. This threshold system applies to general extreme risk management. Finally, a simulation and comparison study demonstrates the good performance of the proposed multivariate extreme quantile estimator. Supplemental materials providing technical details are available online.

In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not been studied thoroughly. The present paper aims at providing conditions under which the BM method can be justified. We also provide a theoretical comparative study of the methods, which is in general consistent with the vast literature on comparing the methods all based on simulated data and fully parametric models. The results indicate that the BM method is a rather efficient method under usual practical conditions. In this paper, we restrict attention to the i.i.d. case and focus on the probability weighted moment (PWM) estimators of Hosking, Wallis and Wood [Technometrics (1985) 27 251-261].

The study has investigated the implications of three estimation methods, namely L-moments, Maximum Likelihood, and Maximum Product of Spacing (MPS), for fitting the four-parameter Kappa Distribution (KAPD) in extreme value analysis using Monte Carlo simulations. The accuracy of the estimates has been evaluated using root mean square error (RMSE) and bias. The paper also includes an analysis of the effect of the estimation method on the estimated quantiles considering a real-life example of annual maximum peak flows and the Generalized Normal Distribution as the error distribution. Assessment metrics of the empirical analysis include standard error, L-scale, and 90% confidence limits of the estimated quantiles. The results reveal that MPS is a preferred method of estimation of parameters for KAPD, i.e. having the lowest RMSE values, especially in the presence of heavier tail and significant positive skewness for small to very large sample sizes. Secondly, the method of L-moments is recommended due to its low bias while analyzing the distribution of shape parameters having a slightly heavier tail, and slight or moderate positive skewness. The results associated with the quality of estimated quantiles using real-life data are consistent with the findings of simulation outcomes.

This paper establishes an asymptotic theory and inference method for quantile treatment effect estimators when the quantile index is close to or equal to zero. Such quantile treatment effects are of interest in many applications, such as the effect of maternal smoking on an infant’s adverse birth outcomes. When the quantile index is close to zero, the sparsity of data jeopardizes conventional asymptotic theory and bootstrap inference. When the quantile index is zero, there are no existing inference methods directly applicable in the treatment effect context. This paper addresses both of these issues by proposing new inference methods that are shown to be asymptotically valid as well as having adequate finite sample properties.

We propose a new nonparametric regression approach that combines deep neural networks with support vector quantile regression models. The nature of deep neural networks enables complex nonlinear regression quantiles to be estimated more accurately. Because deep learning models have a complicated structure, the proposed method can easily fit both smooth and non-smooth data sets. For this reason, we can effectively model data sets with truncated points or locally different smoothness in which spline-based smoothing methods often fail. Stepwise fitting is used to increase computing speed when fitting multiple quantiles. This produces stable fits, especially when observations are scarce near the target quantile. In addition, we employ certain constraints to prevent the fitted quantiles from crossing. The benefits of the proposed method are more apparent when the errors are heteroscedastic, although quantile regression does not require homogeneous errors. We illustrate the flexibility of the proposed method using simulated data sets and six real data examples with univariate and multivariate input variables.

We propose three new estimators of the Weibull distribution parameters which lead to three new plug-in estimators of quantiles. One of them is a modification of the maximum likelihood estimator and two of them are based on nonparametric estimators of the Gini coefficient. We also make some review of estimators of the Weibull distribution parameters and quantiles. We compare the small sample performance (in terms of bias and mean squared error) of the known and new estimators and extreme quantiles. Based on simulations, we obtain, among others, that the proposed modification of the maximum likelihood estimator of the shape parameter has a smaller bias and mean squared error than the maximum likelihood estimator, and is better or as good as known estimators when the sample size is not very small. Moreover, one of the proposed estimator, based on the nonparametric estimator of the Gini coefficient, leads to good extreme quantiles estimates (better than the maximum likelihood estimator) in the case of small sample sizes.

Quantile regression as an alternative to modeling the conditional mean function provides a comprehensive picture of the relationship between a response and covariates. It is particularly attractive in applications focused on the upper or lower conditional quantiles of the response. However, conventional quantile regression estimators are often unstable at the extreme tails, owing to data sparsity, especially for heavy-tailed distributions. Assuming that the functional predictor has a linear effect on the upper quantiles of the response, we develop a novel estimator for extreme conditional quantiles using a functional composite quantile regression based on a functional principal component analysis and an extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator under some regularity conditions, and compare it with other estimation methods using Monte Carlo simulations. Finally, we demonstrate the proposed method by empirically analyzing two real data sets.

Next to the traditional analysis of trends in time series of hydro-climatological variables, analysis of decadal oscillations in these variables is of particular importance for the risk assessment of hydro-climatological disasters and risk-based decision-making. Conventional parametric and nonparametric tests, however, need implementing a set of background assumptions related to serial structure and statistical distribution of data. They neither focus on the extreme events and their probability of occurrence. In order to get rid of these limitations, we suggest a modified version of the Sen Method (SM), combined with the Quantile Perturbation Method (QPM) for examining temporal variation of extreme hydrological events. The developed method is tested for decadal analysis of monthly and annual river flows at 10 hydrometric stations in the Qazvin plain in Iran. The results show oscillatory patterns in extreme river flow quantiles, with a positive anomaly during the 1990s and a negative one during the 2000s. It is also shown that the concurrent use of the two methods allows to set a complete picture on the temporal changes in high and low extremes in historical river flow observations in different seasons.

We consider inference about tail properties of a distribution from an iid sample, based on extreme value theory. All of the numerous previous suggestions rely on asymptotics where eventually, an infinite number of observations from the tail behave as predicted by extreme value theory, enabling the consistent estimation of the key tail index, and the construction of confidence intervals using the delta method or other classic approaches. In small samples, however, extreme value theory might well provide good approximations for only a relatively small number of tail observations. To accommodate this concern, we develop asymptotically valid confidence intervals for high quantile and tail conditional expectations that only require extreme value theory to hold for the largest k observations, for a given and fixed k. Small-sample simulations show that these \"fixed-k\" intervals have excellent small-sample coverage properties, and we illustrate their use with mainland U.S. hurricane data. In addition, we provide an analytical result about the additional asymptotic robustness of the fixed-k approach compared to k n → ∞ inference.