DSpace Collection:http://hdl.handle.net/10316/155442022-09-26T11:54:28Z2022-09-26T11:54:28ZOn automatic kernel density estimate-based tests for goodness-of-fitTenreiro, Carloshttp://hdl.handle.net/10316/1017992022-09-15T20:43:58Z2022-01-01T00:00:00ZTitle: On automatic kernel density estimate-based tests for goodness-of-fit
Authors: Tenreiro, Carlos
Abstract: Although estimation and testing are different statistical problems, if we want to use a test statistic based on the Parzen--Rosenblatt estimator to test the hypothesis that the underlying density function $f$ is a member of a location-scale family of probability density functions, it may be found reasonable to choose the smoothing parameter in such a way that the kernel density estimator is an effective estimator of $f$ irrespective of which of the null or the alternative hypothesis is true. In this paper we address this question by considering the well-known Bickel--Rosenblatt test statistics which are based on the quadratic distance between the nonparametric kernel estimator and two parametric estimators of $f$ under the null hypothesis. For each one of these test statistics we describe their asymptotic behaviours for a general data-dependent smoothing parameter, and we state their limiting gaussian null distribution and the consistency of the associated goodness-of-fit test procedures for location-scale families. In order to compare the finite sample power performance of the Bickel--Rosenblatt tests based on a null hypothesis-based bandwidth selector with other bandwidth selector methods existing in the literature, a simulation study for the normal, logistic and Gumbel null location-scale models is included in this work.2022-01-01T00:00:00ZCommutation Classes of the Reduced Words for the Longest Element of ${\mathfrak S}_n$Gutierres, GonçaloMamede, Ricardo NunoSantos, José Luishttp://hdl.handle.net/10316/1013542022-08-24T20:40:09Z2020-01-01T00:00:00ZTitle: Commutation Classes of the Reduced Words for the Longest Element of ${\mathfrak S}_n$
Authors: Gutierres, Gonçalo; Mamede, Ricardo Nuno; Santos, José Luis
Abstract: Using the standard Coxeter presentation for the symmetric group Sn, two re-
duced expressions for the same group element w are said to be commutationally
equivalent if one expression can be obtained from the other one by applying a nite
sequence of commutations. The commutation classes can be seen as the vertices
of a graph bG
(w), where two classes are connected by an edge if elements of those
classes di er by a long braid relation. We compute the radius and diameter of the
graph bG
(w0), for the longest element w0 in the symmetric group Sn, and show that
it is not a planar graph for n > 6. We also describe a family of commutation classes
which contains all atoms, that is classes with one single element, and a subfamily of
commutation classes whose elements are in bijection with standard Young tableaux
of certain moon-polyomino shapes.2020-01-01T00:00:00ZOn bornological semi-abelian algebrasBorceux, FrancisClementino, Maria Manuelhttp://hdl.handle.net/10316/1012212022-08-17T23:02:27Z2021-01-01T00:00:00ZTitle: On bornological semi-abelian algebras
Authors: Borceux, Francis; Clementino, Maria Manuel
Abstract: If T is a semi-abelian algebraic theory, we prove that the category
BornT of bornological T-algebras is homological with semi-direct products.
We give a formal criterion for the representability of actions in BornT
and, for a bornological T-algebra X, we investigate the relation between the
representability of actions on X as a T-algebra and as a bornological T-
algebra. We investigate further the algebraic coherence and the algebraic
local cartesian closedness of BornT and prove in particular that both properties
hold in the case of bornological groups.2021-01-01T00:00:00ZRegistration of Consecutive Frames From Wireless Capsule Endoscopy for 3D Motion EstimationOliveira, MarinaAraújo, HelderFigueiredo, Isabel N.Pinto, LuísCurto, EvaPerdigoto, Luíshttp://hdl.handle.net/10316/1008752022-07-18T20:38:07Z2021-01-01T00:00:00ZTitle: Registration of Consecutive Frames From Wireless Capsule Endoscopy for 3D Motion Estimation
Authors: Oliveira, Marina; Araújo, Helder; Figueiredo, Isabel N.; Pinto, Luís; Curto, Eva; Perdigoto, Luís
Abstract: Wireless Capsule Endoscopy (WCE) is a non-invasive medical procedure devised for painless
in vivo inspection of the gastrointestinal (GI) tract. It is especially valuable for the examination of the small
intestine since it is dif cult to reach by traditional endoscopic procedures. The setup includes a camera with
an embedded light source and a circuit capable of acquiring and transmitting the video. The main challenge
of this technology is the identi cation of the position and trajectory of the capsule as it travels through the GI
tract, which is particularly relevant during the detection of anomalies in the tissue. Given only the information
provided by the recorded images, it is possible to estimate the 3D motion of the camera capsule and provide
a full trajectory reconstruction. A critical yet dif cult step in this process is the image registration between
sequential frames. Therefore, being able to determine accurate correspondences between points, regions or
features in two consecutive frames is crucial for the computation of the relative rotation and translation of
the capsule. This paper comprises a comparative assessment of methodologies to address this problem with
a porcine colon dataset obtained with our experimental setup.2021-01-01T00:00:00Z