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A way to transform a given copula by means of a univariate function is presented. The resulting copula can be interpreted as the result of a global shock affecting all the components of a system modeled by the original copula. The properties of this copula transformation from the perspective of semi-group action are presented, together with some investigations about the related tail behavior. Finally, the whole methodology is applied to model risk assessment. [ABSTRACT FROM AUTHOR]

Abstract: Let be a random tessellation in , , observed in a bounded Borel subset and be a measurable function defined on the set of convex bodies. A point , called the nucleus of , is associated with each cell of . Applying to all the cells of , we investigate the order statistics of over all cells with nucleus in when goes to infinity. Under a strong mixing property and a local condition on and , we show a general theorem which reduces the study of the order statistics to the random variable , where is the typical cell of . The proof is deduced from a Poisson approximation on a dependency graph via the Chen–Stein method. We obtain that the point process , where and are two suitable functions depending on , converges to a non-homogeneous Poisson point process. Several applications of the general theorem are derived in the particular setting of Poisson–Voronoi and Poisson–Delaunay tessellations and for different functions such as the inradius, the circumradius, the area, the volume of the Voronoi flower and the distance to the farthest neighbor. [Copyright &y& Elsevier]

Abstract: An ensemble statistical post-processor (ESP) is developed for the National Air Quality Forecast Capability (NAQFC) to address the unique challenges of forecasting surface ozone in Baltimore, MD. Air quality and meteorological data were collected from the eight monitors that constitute the Baltimore forecast region. These data were used to build the ESP using a moving-block bootstrap, regression tree models, and extreme-value theory. The ESP was evaluated using a 10-fold cross-validation to avoid evaluation with the same data used in the development process. Results indicate that the ESP is conditionally biased, likely due to slight overfitting while training the regression tree models. When viewed from the perspective of a decision-maker, the ESP provides a wealth of additional information previously not available through the NAQFC alone. The user is provided the freedom to tailor the forecast to the decision at hand by using decision-specific probability thresholds that define a forecast for an ozone exceedance. Taking advantage of the ESP, the user not only receives an increase in value over the NAQFC, but also receives value for costly decisions that the NAQFC couldn't provide alone. [ABSTRACT FROM AUTHOR]

Abstract: Controlling emissions of air pollutants and establishing air quality objectives to improve and protect ambient air quality are very important tasks of Governments. Ozone (O3), one of those pollutants of concern, is not emitted directly into the atmosphere, but is a secondary pollutant produced by reaction between nitrogen dioxide (NO2), hydrocarbons and sunlight. High levels of ozone can produce harmful effects on human health and the environment in general. Therefore, the study of extreme values of ozone represents an important topic of research in environmental problems. Classical extreme value theory has been usually used in air-pollution studies. It consists of fitting a parametric generalized extreme value (GEV) distribution to a data set of extreme values and using the estimated distribution to compute quantities like the probability of exceedance, the quantiles, the return levels or the mean return periods. In this paper, we propose nonparametric methods to estimate those quantities. Additionally, nonparametric estimators of the trends of very high values of ozone are proposed. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) from the UK. Results show that nonparametric estimators work satisfactorily, generally outperforming the behaviour of classical parametric estimators. [ABSTRACT FROM AUTHOR]

Abstract: The study of extreme values and prediction of ozone data is an important topic of research when dealing with environmental problems. Classical extreme value theory is usually used in air-pollution studies. It consists in fitting a parametric generalised extreme value (GEV) distribution to a data set of extreme values, and using the estimated distribution to compute return levels and other quantities of interest. Here, we propose to estimate these values using nonparametric functional data methods. Functional data analysis is a relatively new statistical methodology that generally deals with data consisting of curves or multi-dimensional variables. In this paper, we use this technique, jointly with nonparametric curve estimation, to provide alternatives to the usual parametric statistical tools. The nonparametric estimators are applied to real samples of maximum ozone values obtained from several monitoring stations belonging to the Automatic Urban and Rural Network (AURN) in the UK. The results show that nonparametric estimators work satisfactorily, outperforming the behaviour of classical parametric estimators. Functional data analysis is also used to predict stratospheric ozone concentrations. We show an application, using the data set of mean monthly ozone concentrations in Arosa, Switzerland, and the results are compared with those obtained by classical time series (ARIMA) analysis. [ABSTRACT FROM AUTHOR]

Abstract: In the process of analyzing data, testing the fit of a model under consideration is a prerequisite for performing inference about the model parameters. In this paper we examine the goodness-of-fit testing problem for assessing whether a sample is consistent with the Weibull-type model. Inspired by the Jackson and the Lewis test statistics, originally proposed as goodness-of-fit tests for the exponential distribution, we introduce two new statistics for testing Weibull-type behavior, and study their asymptotic properties. Moreover, given that the statistics are ratios of estimators for the Weibull-tail coefficient, we obtain new estimators for the latter, and establish their consistency and asymptotic normality. The small sample behavior of our statistics and estimators is evaluated on the basis of a simulation study. [Copyright &y& Elsevier]

Abstract: This paper proves weak convergence in of the tail empirical process–the renormalized extreme tail of the empirical process–for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on long range dependence (absolute regularity or strong mixing), and (iii) convergence of the covariance function. We further show how the limit process is changed if exceedances of a nonrandom level are replaced by exceedances of a high quantile of the observations. Weak convergence of the tail empirical process is one key to asymptotics for extreme value statistics and its wide range of applications, from geoscience to finance. [Copyright &y& Elsevier]

Abstract: We study the Kolmogorov–Smirnov test, Berk–Jones test, score test and their integrated versions in the context of testing the goodness-of-fit of a heavy tailed distribution function. A comparison of these tests is conducted via Bahadur efficiency and simulations. In the simulations, the score test and the integrated score test show the best performance. Although the Berk–Jones test is more powerful than the Kolmogorov–Smirnov test, this does not hold true for their integrated versions; this differs from results in Einmahl et al. [2003. Empirical likelihood based hypothesis testing. Bernoulli 9(2), 267–290], which shows the difference of Berk–Jones test in testing distributions and tails. [Copyright &y& Elsevier]

We propose a method for the analysis of a spatial point pattern, which is assumed to arise as a set of observations from a spatial nonhomogeneous Poisson process. The spatial point pattern is observed in a bounded region, which, for most applications, is taken to be a rectangle in the space where the process is defined. The method is based on modeling a density function, defined on this bounded region, that is directly related with the intensity function of the Poisson process. We develop a flexible nonparametric mixture model for this density using a bivariate Beta distribution for the mixture kernel and a Dirichlet process prior for the mixing distribution. Using posterior simulation methods, we obtain full inference for the intensity function and any other functional of the process that might be of interest. We discuss applications to problems where inference for clustering in the spatial point pattern is of interest. Moreover, we consider applications of the methodology to extreme value analysis problems. We illustrate the modeling approach with three previously published data sets. Two of the data sets are from forestry and consist of locations of trees. The third data set consists of extremes from the Dow Jones index over a period of 1303 days. [Copyright &y& Elsevier]

Abstract: In this paper, we derive sharp upper bounds on expectations of non-adjacent increments of second record statistics based on independent samples from decreasing density families of distributions. We also determine the distributions for which the bounds are attained. These bounds are based on a projection method. [Copyright &y& Elsevier]

Abstract: Weighted approximations to the tail of the distribution function and its empirical counterpart are derived which are suitable for applications in extreme value statistics. The approximation of the tail empirical distribution function is then used to develop an Anderson–Darling type test of the null hypothesis that the distribution function belongs to the domain of attraction of an extreme value distribution. [Copyright &y& Elsevier]

Abstract: We consider an i.i.d. sample, from an underlying distribution function with unknown shape, location and scale parameters, belonging to some max-domain of attraction. We study the performance of a test statistic which is merely a ratio between the maximum and the mean of the sample of the excesses above some random threshold. This scale/location invariant ratio turns out to be very useful in the construction of an asymptotically size test for the null hypothesis that the distribution comes from the Gumbel domain of attraction. The test is based on the largest observations, where is any intermediate sequence of positive integers. Both power of the test and type I error probability are studied for finite sample sizes by simulation. [Copyright &y& Elsevier]

Abstract: Standard control charts are often seriously in error when the distributional form of the observations differs from normality. Recently, control charts have been developed for larger parametric families. A third possibility is to apply a suitable (modified version of a) nonparametric control chart. This paper deals with the question when to switch from the control chart based on normality to a parametric control chart, or even to a nonparametric one. This model selection problem is solved by using the estimated model error as yardstick. It is shown that the new combined control chart asymptotically behaves as each of the specific control charts in their own domain. Simulations exhibit that the combined control chart performs very well under a great variety of distributions and hence it is recommended as an omnibus control chart, nicely adapted to the distribution at hand. The combined control chart is illustrated by an application on real data. The new modified nonparametric control chart is an attractive alternative and can be recommended as well. [Copyright &y& Elsevier]

Abstract: Two distribution-free estimators are proposed to estimate the mean of a dependent variable after fitting a semiparametric two-part heteroscedastic regression model to a transformation of the dependent variable. We show that the proposed estimators are consistent and have asymptotic normal distributions. We also compare their finite-sample performance in a simulation study. Finally, we illustrate the proposed methods in a real-world example of predicting in-patient health care costs. [Copyright &y& Elsevier]

Abstract: We consider estimation of the tail index parameter from i.i.d. observations in Pareto and Weibull type models, using a local and asymptotic approach. The slowly varying function describing the non-tail behavior of the distribution is considered as an infinite dimensional nuisance parameter. Without further regularity conditions, we derive a local asymptotic normality (LAN) result for suitably chosen parametric submodels of the full semiparametric model. From this result, we immediately obtain the optimal rate of convergence of tail index parameter estimators for more specific models previously studied. On top of the optimal rate of convergence, our LAN result also gives the minimal limiting variance of estimators (regular for our parametric model) through the convolution theorem. We show that the classical Hill estimator is regular for the submodels introduced with limiting variance equal to the induced convolution theorem bound. We also discuss the Weibull model in this respect. [Copyright &y& Elsevier]

Abstract: The large claims reinsurance treaties ECOMOR and LCR are well known not to be very popular. They have been largely neglected by most reinsurers because of their technical complexity. In this paper, we derive new mathematical results connected to asymptotic problems of these reinsurance forms. Perhaps these results can reopen the discussion on the usefulness of including the largest claims in the decision making procedure. Apart from asymptotic estimates for the tail of the distribution of the ECOMOR-quantity, we find its weak laws. We also deal with the weak laws of the LCR-quantity. Finally, we illustrate the outcomes with a number of simulations. [Copyright &y& Elsevier]

Abstract: The Weibull distribution is widely used in lifetime data analysis. For example, in studies on the time to the occurrence of tumors in human populations or in laboratory animals, the time of occurrence of tumors is generally assumed to be distributed as a Weibull distribution. Moreover, in engineering, the voltage levels at which failure occurred in electrical cable insulation has been shown to be distributed as a Weibull distribution. When comparing two independent Weibull distributions, it is often assumed that only the scale parameter is altered. In this paper, we propose a simple and accurate procedure to obtain inference concerning the ratio of the two scale parameters of two independent distributions. The performance of the proposed method is assessed through Monte Carlo simulation studies. The numerical results show that the proposed method is extremely accurate even for very small samples. The method is applied to a set of real-life data. [Copyright &y& Elsevier]

Abstract: This paper provides upper sharp bounds for the mean of the total time on test based on type II censoring samples in terms of various scale units. It also presents numerical evaluation of the so obtained bounds. [Copyright &y& Elsevier]

Abstract: Assume that are iid rv''s with continuous cumulative distribution function and finite th absolute moment. The aim of the paper is to present sharp upper bounds for expectations of increments of record values, measured in various scale units. We also derive the bounds in case when the parent distribution has monotone density and or monotone failure rate. The distribution functions attaining the bounds are characterized. [Copyright &y& Elsevier]

The projection method is applied to establish sharp p-norm bounds, measured in terms of scale units generated by absolute central population moments for the expectations of record increments. The bounds are derived based on combining the Moriguti monotone approximation of functions with the Hölder inequality applied for the proper integral representations of expected record increments. The projection p-norm bounds are numerically evaluated and compared with other classical bounds. [Copyright &y& Elsevier]

We prove a second-order approximation formula for the distribution of the largest term among an infinite moving average Gaussian sequence. The second-order correction term depends on the autocovariance function only through the second largest autocovariance. Applications to Gaussian time series are discussed and a simulation study showed a substantial improvement over other approximations to the exact distribution of the maximum. [Copyright &y& Elsevier]