Alberto Rodríguez Casal

Publications (15) View all

• Article: CircSiZer: an exploratory tool for circular data

  María Oliveira, Rosa M. Crujeiras, Alberto Rodríguez-Casal
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  ABSTRACT: Smoothing methods and SiZer (SIgnificant ZERo crossing of the derivatives) are useful tools for exploring significant underlying structures in data samples. An extension of SiZer to circular data, namely CircSiZer, is introduced. Based on scale-space ideas, CircSiZer presents a graphical device to assess which observed features are statistically significant, both for density and regression analysis with circular data. The method is intended for analyzing the behavior of wind direction in the atlantic coast of Galicia (NW Spain) and how it has an influence over wind speed. The performance of CircSiZer is also checked with some simulated examples.
  Environmental and Ecological Statistics 04/2013; · 1.31 Impact Factor
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  Available from: Alberto Rodríguez Casal

  Article: Recovering the shape of a point cloud in the plane

  Beatriz Pateiro-López, Alberto Rodríguez Casal
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  ABSTRACT: In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the existence of a separating hyperplane for each exterior point we assume the existence of a separating open ball with radius alpha. Given an alpha-convex set S, the alpha-convex hull of independent random points in S is the natural estimator of the set. If alpha is unknown the r_n-convex hull of the sample can be considered. We analyze the asymptotic properties of the r_n-convex hull estimator in the bidimensional case and obtain the convergence rate for the expected distance in measure between the set and the estimator. The geometrical complexity of the estimator and its dependence on r_n is also obtained via the analysis of the expected number of vertices of the r_n-convex hull.
  Test 03/2013; 22(1):19-45. · 1.13 Impact Factor
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  Available from: Ricardo Fraiman

  Article: A nonparametric approach to the estimation of lengths and surface areas

  Antonio Cuevas, Ricardo Fraiman, Alberto Rodríguez-Casal
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  ABSTRACT: The Minkowski content $L_0(G)$ of a body $G\subset{\mathbb{R}}^d$ represents the boundary length (for $d=2$) or the surface area (for $d=3$) of $G$. A method for estimating $L_0(G)$ is proposed. It relies on a nonparametric estimator based on the information provided by a random sample (taken on a rectangle containing $G$) in which we are able to identify whether every point is inside or outside $G$. Some theoretical properties concerning strong consistency, $L_1$-error and convergence rates are obtained. A practical application to a problem of image analysis in cardiology is discussed in some detail. A brief simulation study is provided.
  The Annals of Statistics 09/2007; 35(1031):1051. · 3.03 Impact Factor
• Article: Generalizing the Convex Hull of a Sample: The R Package alphahull

  Pateiro-López Beatriz, Rodríguez-Casal Alberto
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  ABSTRACT: This paper presents the R package alphahull which implements the α-convex hull and the α-shape of a finite set of points in the plane. These geometric structures provide an informative overview of the shape and properties of the point set. Unlike the convex hull, the α-convex hull and the α-shape are able to reconstruct non-convex sets. This flexibility make them specially useful in set estimation. Since the implementation is based on the intimate relation of theses constructs with Delaunay triangulations, the R package alphahull also includes functions to compute Voronoi and Delaunay tesselations. The usefulness of the package is illustrated with two small simulation studies on boundary length estimation.
  Journal of statistical software 04/2010; 34(5):1-28. · 4.01 Impact Factor
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  Available from: Rosa M. Crujeiras

  Article: A plug-in rule for bandwidth selection in circular density estimation

  M. Oliveira, R. M. Crujeiras, A. Rodríguez-Casal
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  ABSTRACT: A new plug-in rule procedure for bandwidth selection in kernel circular density estimation is introduced. The performance of this proposal is checked throughout a simulation study considering a variety of circular distributions exhibiting multimodality, peakedness and/or skewness. The plug-in rule behaviour is also compared with other existing bandwidth selectors. The method is illustrated with two classical datasets of cross-beds layers and animal orientation.
  Computational Statistics & Data Analysis 12/2012; 56(12):3898–3908. · 1.03 Impact Factor