A hierarchical Bayesian approach to robust parameter design.

The goal of robust parameter design experiments is to identify significant location and dispersion factors that can be used to set the mean response at the target level and to decrease the sensitivity of the response to uncontrolled noise factors. We present a hierarchical Bayesian model and use empirical Bayes priors to find the active factors and to get reliable estimates of the location and dispersion parameters. The approach is particularly useful when the design points are not replicated, a case which is challenging with standard procedures.Bayesian; Credibility or posterior probability intervals; Design; Empirical Bayes priors; Factors; Gibbs sampling; Hierarchical Bayesian model; Location and dispersion factors; Model; Noise; Parameters; Sensitivity; Taguchi experiments; WinBUGS;

On kernel estimation of the second order rate parameter in multivariate extreme value statistics

International audienceWe introduce a flexible class of kernel type estimators of a second order parameter appearing in the multivariate extreme value framework. Such an estimator is crucial in order to construct asymptotically unbiased estimators of dependence measures, as e.g. the stable tail dependence function. We establish the asymptotic properties of this class of estimators under suitable assumptions. The behaviour of some examples of kernel estimators is illustrated by a simulation study in which they are also compared with a benchmark estimator of a second order parameter recently introduced in the literature

Dispersion Models for Extremes

We propose extreme value analogues of natural exponential families and exponential dispersion models, and introduce the slope function as an analogue of the variance function. The set of quadratic and power slope functions characterize well-known families such as the Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fr\'echet. We show a convergence theorem for slope functions, by which we may express the classical extreme value convergence results in terms of asymptotics for extreme dispersion models. The main idea is to explore the parallels between location families and natural exponential families, and between the convolution and minimum operations.Comment: 23 pages. Abstract submitted to the 56th Session of the ISI, Lisboa, 200

Bias-corrected and robust estimation of the bivariate stable tail dependence function

We consider the estimation of the bivariate stable tail dependence function and propose a bias-corrected and robust estimator. We establish its asymptotic behavior under suitable assumptions. The finite sample performance of the proposed estimator is examined on a simulation study involving both uncontaminated and contaminated samples

Conditional marginal expected shortfall

In the context of bivariate random variables (Y^{(1)},Y^{(2)}), the marginal expected shortfall, defined as E(Y^{(1)}|Y^{(2)} \ge Q_2(1-p)) for p small, where Q_2 denotes the quantile function of Y^{(2)}, is an important risk measure, which finds applications in areas like, e.g., finance and environmental science. We consider estimation of the marginal expected shortfall when the random variables of main interest (Y^{(1)},Y^{(2)}) are observed together with a random covariate X, leading to the concept of the conditional marginal expected shortfall. The asymptotic behavior of an estimator for this conditional marginal expected shortfall is studied for a wide class of conditional bivariate distributions, with heavy-tailed marginal conditional distributions, and where p tends to zero at an intermediate rate. The finite sample performance is evaluated on a small simulation experiment. The practical applicability of the proposed estimator is illustrated on flood claim data

Tail Dependence Measure for Examining Financial Extreme Co-movements

Modeling and forecasting extreme co-movements in financial market is important for conducting stress test in risk management. Asymptotic independence and asymptotic dependence behave drastically different in modeling such co-movements. For example, the impact of extreme events is usually overestimated whenever asymptotic dependence is wrongly assumed. On the other hand, the impact is seriously underestimated whenever the data is misspecified as asymptotic independent. Therefore, distinguishing between asymptotic independence/dependence scenarios is very informative for any decision-making and especially in risk management. We investigate the properties of the limiting conditional Kendall’s tau which can be used to detect the presence of asymptotic independence/dependence. We also propose nonparametric estimation for this new measure and derive its asymptotic limit. A simulation study shows good performances of the new measure and its combination with the coefficient of tail dependence proposed by Ledford and Tawn (1996, 1997). Finally, applications to financial and insurance data are provided

Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions

A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and Conditional Tail Moments. Trimmed and winsorised versions of the empirical counterparts of extreme analogues of Wang distortion risk measures are considered. Their asymptotic properties are analysed, and it is shown that it is possible to construct corrected versions of trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in difficult finite-sample situations when the underlying distribution has a very heavy right tail. This technique is showcased on a set of real fire insurance data

Reduced-Bias Location-Invariant Extreme Value Index Estimation: A Simulation Study

In this article, we deal with semi-parametric corrected-bias estimation of a positive extreme value index (EVI), the primary parameter in statistics of extremes. Under such a context, the classical EVI-estimators are the Hill estimators, based on any intermediate number k of top-order statistics. But these EVI-estimators are not location-invariant, contrarily to the PORT-Hill estimators, which depend on an extra tuning parameter q, with 0 ≤ q < 1, and where PORT stands for peaks over random threshold. On the basis of second-order minimum-variance reduced-bias (MVRB) EVI-estimators, we shall here consider PORT-MVRB EVI-estimators. Due to the stability on k of the MVRB EVI-estimates, we propose the use of a heuristic algorithm, for the adaptive choice of k and q, based on the bias pattern of the estimators as a function of k. Applications in the fields of insurance and finance will be provided.Research partially supported by FCT/OE and PTDC/FEDER.publishe

On the study of extremes with dependent random right-censoring

The study of extremes in missing data frameworks is a recent developing field. In particular, the randomly right-censored case has been receiving a fair amount of attention in the last decade. All studies on this topic, however, essentially work under the usual assumption that the variable of interest and the censoring variable are independent. Furthermore, a frequent characteristic of estimation procedures developed so far is their crucial reliance on particular properties of the asymptotic behaviour of the response variable Z (that is, the minimum between time-to-event and time-to-censoring) and of the probability of censoring in the right tail of Z. In this paper, we focus instead on elucidating this asymptotic behaviour in the dependent censoring case, and, more precisely, when the structure of the dependent censoring mechanism is given by an extreme value copula. We then draw a number of consequences of our results, related to the asymptotic behaviour, in this dependent context, of a number of estimators of the extreme value index of the random variable of interest that were introduced in the literature under the assumption of independent censoring, and we discuss more generally the implications of our results on the inference of the extremes of this variable

Rituele uitbeelding van Etruskische demonen van de dood, of vrouwelijk aandeel in de magische krijgsverrichtingen : een mentaliteitsvraagstuk

Goegebeur Werner. Rituele uitbeelding van Etruskische demonen van de dood, of vrouwelijk aandeel in de magische krijgsverrichtingen : een mentaliteitsvraagstuk. In: Revue belge de philologie et d'histoire, tome 60, fasc. 1, 1982. Antiquité — Oudheid. pp. 51-100