Nonparametric estimation of multivariate extreme-value copulas

Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to certain shape constraints that arise from an integral transform of an underlying measure called spectral measure. Multivariate extensions are provided of certain rank-based nonparametric estimators of the Pickands dependence function. The shape constraint that the estimator should itself be a Pickands dependence function is enforced by replacing an initial estimator by its best least-squares approximation in the set of Pickands dependence functions having a discrete spectral measure supported on a sufficiently fine grid. Weak convergence of the standardized estimators is demonstrated and the finite-sample performance of the estimators is investigated by means of a simulation experiment.     

The role of individual and organizational characteristics in feedback seeking behaviour in the initial career stage

The present study investigates whether the frequency by which employees seek informal feedback and the quality of the self-initiated feedback influences perceived career development. Furthermore, we investigated goal orientation and perceived learning culture, as antecedents of feedback seeking behaviour. Data were collected from 116 financial experts from various multinational corporations worldwide. Results show that particularly the quality of self-initiated feedback from supervisors positively affects perceived career development. The quality of self-initiated feedback from supervisors mediates the relation between the perceived learning culture and perceived career development. Furthermore, learning goal orientation directly relates to perceived career development. Last, our results highlight the significance of creating a learning culture in which informal feedback is stimulated. Implications of these findings are discussed.     

Development and Psychometric Properties of the Classroom Peer Context Questionnaire

Children's view on the peer context in their classroom may differ from that of other informants, but no measure systematically examines children's own view. Therefore, we developed the Classroom Peer Context Questionnaire (CPCQ) and evaluated its reliability, validity, and stability in two studies. In Study 1, 464 children (M_age = 10.8 years, 53.2% girls) from 18 Grade 5 classrooms participated in 2 waves of data collection. In Study 2, 1538 children (M_age = 10.6 years, 47.2% girls) from 59 Grade 5 classrooms participated in 3 waves of data collection. Exploratory factor analyses in Study 1 revealed 5 dimensions labeled comfort, cooperation, conflict, cohesion, and isolation. Confirmatory factor analyses in Study 2 supported these 5 dimensions. Study 2 also demonstrated good reliability, validity, and stability for each dimension. Researchers and professionals in schools may use the CPCQ to obtain reliable and quick information on how children perceive the peer context in their classroom.     

Projection estimators of Pickands dependence functions

The authors consider the construction of intrinsic estimators for the Pickands dependence function of an extreme‐value copula. They show how an arbitrary initial estimator can be modified to satisfy the required shape constraints. Their solution consists in projecting this estimator in the space of Pickands functions, which forms a closed and convex subset of a Hilbert space. As the solution is not explicit, they replace this functional parameter space by a sieve of finite‐dimensional subsets. They establish the asymptotic distribution of the projection estimator and its finite‐dimensional approximations, from which they conclude that the projected estimator is at least as efficient as the initial one.     

Large‐sample tests of extreme‐value dependence for multivariate copulas

Starting from the characterization of extreme‐value copulas based on max‐stability, large‐sample tests of extreme‐value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p‐values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite‐sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi et al. (1998) recently revisited by Ben Ghorbal et al. (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data. The Canadian Journal of Statistics 39: 703–720; 2011. © 2011 Statistical Society of Canada     

Second-order refined peaks-over-threshold modelling for heavy-tailed distributions

Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit well and in such a case applies only to a small upper fraction of the data. The extension of the (G)PD proposed in this paper is able to describe the excess distribution for lower thresholds in case of heavy-tailed distributions. This yields a statistical model that can be fitted to a larger portion of the data. Moreover, estimates of tail parameters display stability for a larger range of thresholds. Our findings are supported by asymptotic results, simulations and a case study.     

A Euclidean Likelihood Estimator for Bivariate Tail Dependence

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the spectral measure which is simple and explicitly defined, with its expression being free of Lagrange multipliers. Our estimator is shown to have the same limit distribution as the maximum empirical likelihood estimator of Einmahl and Segers (2009 Einmahl , J. H. J. , Segers , J. ( 2009 ). Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution . Ann. Statist. 37 ( 5B ): 2953 – 2989 .[Crossref], [Web of Science ®] , [Google Scholar]). Numerical experiments suggest an overall good performance and identical behavior to the maximum empirical likelihood estimator. We illustrate the method in an extreme temperature data analysis.     

Inference for clusters of extreme values

Summary. Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of declustering scheme often has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated before declustering, and supports a bootstrap procedure for assessing the variability of estimates.     

Working on professional development of faculty staff in higher education: investigating the relationship between social informal learning activities and employability

In this study, we examined how social informal learning and formal learning of faculty staff in higher education relate to their employability. Data were collected from 209 faculty staff members working at a Dutch university. Results showed that social informal learning was related to the employability of faculty staff. Further analysis revealed that especially external information seeking and acting upon feedback from colleagues and not formal learning predicted the employability of faculty staff. The finding suggests that institutes of higher education should especially foster the professional development of their faculty staff by stimulating exchange of information and seeking and using feedback with colleagues in a proactive manner.     

The use of a personal development plan and the undertaking of learning activities,expertise-growth,flexibility and performance: the role of supporting assessment conditions

In the current search for tools that encourage and assess learning and development, personal development plans (PDPs) are being used ever more frequently by organizations. A PDP is an assessment tool used by the employee to reflect on, to document the competencies s/he has been working on and to present his/her plans for further development. This study conducted among employees working in a governmental organization in the Netherlands (N = 287) focused on the PDP practice as conceptualized by three supporting conditions: learning and reflection, information and feedback and the motivating supervisor. It examined which of these features enhance the undertaking of learning activities, expertise-growth, flexibility towards changing circumstances and performance. Results from the hierarchical regression analyses indicate that a motivating supervisor, information and feedback and reflection by the employee on the basis of his/her PDP affect whether or not a PDP contributes to the four measured output variables. Next, by conducting mediation analyses evidence is found for the mediating role of undertaking learning activities in the relation between the PDP practice and two output variables.