On the Hill estimator: a comparison of methods

Extreme value theory (EVT) deals with the occurrence of extreme phenomena. The tail index is a very important parameter appearing in the estimation of the probability of rare events. Under a semiparametric framework, inference requires the choice of a number k of upper order statistics to be considered. This is the crux of the matter and there is no definite formula to do it, since a small k leads to high variance and large values of k tend to increase the bias. Several methodologies have emerged in literature, specially concerning the most popular Hill estimator (Hill, 1975). In this work we compare through simulation well-known procedures presented in Drees and Kaufmann (1998), Matthys and Beirlant (2000), Beirlant et al. (2002) and de Sousa and Michailidis (2004), with a heuristic scheme considered in Frahm et al. (2005) within the estimation of a different tail measure but with a similar context. We will see that the new method may be an interesting alternative.

Short-term corneal changes with gas-permeable contact lens wear in keratoconus subjects: a comparison of two fitting approaches

Purpose: To evaluate changes in anterior corneal topography and higher-order aberrations (HOA) after 14-days of rigid gas-permeable (RGP) contact lens (CL) wear in keratoconus subjects comparing two different fitting approaches. Methods: Thirty-one keratoconus subjects (50 eyes) without previous history of CL wear were recruited for the study. Subjects were randomly fitted to either an apical-touch or three-pointtouch fitting approach. The lens’ back optic zone radius (BOZR) was 0.4 mm and 0.1 mm flatter than the first definite apical clearance lens, respectively. Differences between the baseline and post-CL wear for steepest, flattest and average corneal power (ACP) readings, central corneal astigmatism (CCA), maximum tangential curvature (KTag), anterior corneal surface asphericity, anterior corneal surface HOA and thinnest corneal thickness measured with Pentacam were compared. Results: A statistically significant flattening was found over time on the flattest and steepest simulated keratometry and ACP in apical-touch group (all p < 0.01). A statistically significant reduction in KTag was found in both groups after contact lens wear (all p < 0.05). Significant reduction was found over time in CCA (p = 0.001) and anterior corneal asphericity in both groups (p < 0.001). Thickness at the thinnest corneal point increased significantly after CL wear (p < 0.0001). Coma-like and total HOA root mean square (RMS) error were significantly reduced following CL wearing in both fitting approaches (all p < 0.05). Conclusion: Short-term rigid gas-permeable CL wear flattens the anterior cornea, increases the thinnest corneal thickness and reduces anterior surface HOA in keratoconus subjects. Apicaltouch was associated with greater corneal flattening in comparison to three-point-touch lens wear.

Pointlike reducibility of pseudovarieties of the form V*D

In this paper, we investigate the reducibility property of semidirect products of the form V *D relatively to (pointlike) systems of equations of the form x1 =...= xn, where D denotes the pseudovariety of definite semigroups. We establish a connection between pointlike reducibility of V*D and the pointlike reducibility of the pseudovariety V. In particular, for the canonical signature consisting of the multiplication and the (omega-1)-power, we show that V*D is pointlike-reducible when V is pointlike-reducible.

Neurocognitive profile and cognitive intervention in Alzheimer's disease

Tese de Doutoramento em Psicologia (Especialidade de Psicologia Clínica)

Hume e o problema moral

Tese de Doutoramento em Filosofia (área de especialização em Filosofia Moderna e Contemporânea).

O direito fundamental à proteção na velhice através dos impostos

Dissertação de mestrado em Direito das Crianças, Família e Sucessões