Johan Segers

Inference for clusters of extreme values

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.

Impact of inspiratory muscle training in patients with COPD: what is the evidence?

A meta-analysis including 32 randomised controlled trials on the effects of inspiratory muscle training (IMT) in chronic obstructive pulmonary disease (COPD) patients was performed. Overall and subgroup analyses with respect to training modality (strength or endurance training, added to general exercise training) and patient characteristics were performed. Significant improvements were found in maximal inspiratory muscle strength (PI,max; +13 cmH2O), endurance time (+261 s), 6- or 12-min walking distance (+32 and +85 m respectively) and quality of life (+3.8 units). Dyspnoea was significantly reduced (Borg score -0.9 point; Transitional Dyspnoea Index +2.8 units). Endurance exercise capacity tended to improve, while no effects on maximal exercise capacity were found. Respiratory muscle endurance training revealed no significant effect on PI,max, functional exercise capacity and dyspnoea. IMT added to a general exercise programme improved PI,max significantly, while functional exercise capacity tended to increase in patients with inspiratory muscle weakness (PI,max <60 cmH2O). IMT improves inspiratory muscle strength and endurance, functional exercise capacity, dyspnoea and quality of life. Inspiratory muscle endurance training was shown to be less effective than respiratory muscle strength training. In patients with inspiratory muscle weakness, the addition of IMT to a general exercise training program improved PI,max and tended to improve exercise performance.

Skeletal muscle weakness, exercise tolerance and physical activity in adults with cystic fibrosis

The aim of the present study was to investigate the prevalence of muscle weakness and the importance of physical inactivity in cystic fibrosis (CF), and its relationship to exercise tolerance and muscle strength. Exercise tolerance, skeletal and respiratory muscle strength were studied in a group of 64 adults with CF (age 26±8 yrs, FEV1 % predicted 65±19) and in 20 age-matched controls. Physical activity (PA) was assessed in 20 patients and all controls. Quadriceps muscle weakness was present in 56% of the patients. Peak oxygen uptake and 6-min walking distance were below normal in 89 and 75% of patients, respectively. Respiratory muscle strength was normal. The differences remained after correcting for PA. Quadriceps force was correlated to the 6-min walking distance but not to peak oxygen uptake. “Mild” PA (>3 metabolic equivalents (METS)) and the number of steps overlapped with controls, but CF patients had less moderate PA (>4.8 METS). Moderate PA was related to peak oxygen uptake and quadriceps force. Skeletal muscle weakness and exercise intolerance are prevalent in cystic fibrosis. Physical inactivity is a factor significantly contributing to exercise tolerance and skeletal muscle force in adults with cystic fibrosis, but these impairments are in excess to that expected from physical inactivity only.

Asymptotics of empirical copula processes under non-restrictive smoothness assumptions

Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is non-restrictive in the sense that it is needed anyway to ensure that the candidate limiting process exists and has continuous trajectories. In addition, resampling methods based on the multiplier central limit theorem, which require consistent estimation of the first-order derivatives, continue to be valid. Under certain growth conditions on the second-order partial derivatives that allow for explosive behavior near the boundaries, the almost sure rate in Stute’s representation of the empirical copula process can be recovered. The conditions are verified, for instance, in the case of the Gaussian copula with full-rank correlation matrix, many Archimedean copulas, and many extreme-value copulas.

Extreme-value copulas

Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise naturally in the domain of extreme-value theory, they can also be a convenient choice to model general positive dependence structures. The aim of this survey is to present the reader with the state-of-the-art in dependence modeling via extreme-value copulas. Both probabilistic and statistical issues are reviewed, in a nonparametric as well as a parametric context.

Tails of multivariate Archimedean copulas

A complete and user-friendly directory of tails of Archimedean copulas is presented which can be used in the selection and construction of appropriate models with desired properties. The results are synthesized in the form of a decision tree: Given the values of some readily computable characteristics of the Archimedean generator, the upper and lower tails of the copula are classified into one of three classes each, one corresponding to asymptotic dependence and the other two to asymptotic independence. For a long list of single-parameter families, the relevant tail quantities are computed so that the corresponding classes in the decision tree can easily be determined. In addition, new models with tailor-made upper and lower tails can be constructed via a number of transformation methods. The frequently occurring category of asymptotic independence turns out to conceal a surprisingly rich variety of tail dependence structures.

Rank-based Inference for Bivariate Extreme-value Copulas

Consider a continuous random pair (X, Y ) whose dependence is characterized by an extreme-value copula with Pickands dependence function A. When the marginal distributions of X and Y are known, several consistent estimators of A are available. Most of them are variants of the estimators due to Pickands [Bull. Inst. Internat. Statist. 49 (1981) 859–878] and Cap´era`a, Foug`eres and Genest [Biometrika 84 (1997) 567–577]. In this paper, rank-based versions of these estimators are proposed for the more common case where the margins of X and Y are unknown. Results on the limit behavior of a class of weighted bivariate empirical processes are used to show the consistency and asymptotic normality of these rank-based estimators. Their finite- and large-sample performance is then compared to that of their known-margin analogues, as well as with endpoint-corrected versions thereof. Explicit formulas and consistent estimates for their asymptotic variances are also suggested

Interobserver agreement of medical research council sum-score and handgrip strength in the intensive care unit

Introduction: Muscle weakness often complicates critical illness and is associated with devastating short‐ and long‐term consequences. For interventional studies, reliable measurements of muscle force in the intensive care unit (ICU) are needed. Methods: To examine interobserver agreement, two observers independently measured Medical Research Council (MRC) sum‐score (n = 75) and handgrip strength (n = 46) in a cross‐sectional ICU sample. Results: The intraclass correlation coefficient (ICC) for MRC sum‐score was 0.95 (0.92–0.97). The kappa coefficient for identifying “significant weakness” (MRC sum‐score <48, MRC subtotal upper limbs <24) and “severe weakness” (MRC sum‐score <36) was 0.68 ± 0.09, 0.88 ± 0.07, and 0.93 ± 0.07, respectively. The ICC for left and right handgrip strength was 0.97 (0.94–0.98) and 0.93 (0.86–0.97), respectively. Conclusions: Interobserver agreement on MRC sum‐score and handgrip strength in the ICU was very good. Agreement on “severe weakness” (MRC sum‐score <36) was excellent and supports its use in interventional studies. Agreement on “significant weakness” (MRC sum‐score <48) was good, but even better using the equivalent cut‐off in the upper limbs. It remains to be determined whether this may serve as a substitute. Muscle Nerve 45: 18–25, 2012

Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution.For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to convergence of the corresponding lower tail dependence copulas to the Clayton copula.In this paper, these characterizations are refined and extended to the case of generators which are not necessarily continuously differentiable.Moreover, a counterexample is constructed showing that even if the generator of a strict Archimedean copula is continuously differentiable and slowly varying at the origin, then the lower tail dependence copulas do not need to converge to the independent copula.

Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution

Consider a random sample from a bivariate distribution function