The tangent classifier

This is an Author's Accepted Manuscript of an article published in The American Statistician 66.3 (2012): 185-194 Copyright Taylor and Francis, available online at: http://www.tandfonline.com

Tests for stochastic orders and mean order statistics

This is an Author's Accepted Manuscript of an article published in Commumications in Statistics-Theory and Methods 41.8 (2012):1497-1509 Copyright Taylor and Francis, available online at: http://www.tandfonline.com

Principal components for multivariate functional data

This is the author's version of a work that was accepted for publication in Computational Statistics and Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in COMPUTATIONAL STATISTICS AND DATA ANALYSIS, Vol 55, Issue 9, (2011) http://dx.doi.org/10.1016/j.csda.2011.03.01

The mRMR variable selection method: a comparative study for functional data

The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the ‘most representative’ or ‘most relevant’ variables. However, it is also clear that a purely relevance-oriented criterion could lead to select many redundant variables. The minimum Redundance Maximum Relevance (mRMR) procedure, proposed by Ding and Peng (2005) and Peng et al. (2005) is an algorithm to systematically perform variable selection, achieving a reasonable trade-off between relevance and redundancy. In its original form, this procedure is based on the use of the so-calledmutual information criterion to assess relevance and redundancy. Keeping the focus on functional data problems, we propose here a modified version of the mRMR method, obtained by replacing the mutual information by the new association measure (called distance correlation) suggested by Székely et al. (2007). We have also performed an extensive simulation study, including 1600 functional experiments (100 functional models x 4 sample sizes x 4 classifiers) and three real-data examples aimed at comparing the different versions of the mRMR methodology. The results are quite conclusive in favour of the new proposed alternativeThis research has been partially supported by Spanish grant MTM2010- 1736

Shape classification based on interpoint distance distributions

According to Kendall (1989), in shape theory, The idea is to filter out effects resulting from translations, changes of scale and rotations and to declare that shape is “what is left”.While this statement applies in principle to classical shape theory based on landmarks, the basic idea remains also when other approaches are used. For example, we might consider, for every shape, a suitable associated function which, to a large extent, could be used to characterize the shape. This finally leads to identify the shapes with the elements of a quotient space of sets in such a way that all the sets in the same equivalence class share the same identifying function. In this paper, we explore the use of the interpoint distance distribution (i.e. the distribution of the distance between two independent uniform points) for this purpose. This idea has been previously proposed by other authors [e.g., Osada et al. (2002), Bonetti and Pagano (2005)]. We aim at providing some additional mathematical support for the use of interpoint distances in this context. In particular, we show the Lipschitz continuity of the transformation taking every shape to its corresponding interpoint distance distribution. Also, we obtain a partial identifiability result showing that, under some geometrical restrictions, shapes with different planar area must have different interpoint distance distributions. Finally, we address practical aspects including a real data example on shape classification in marine biologyThis work has been partially supported by Spanish Grants MTM2013-44045-P (Berrendero and Cuevas) and MTM2013-41383-P (Pateiro-López

Testing uniformity for the case of a planar unknown support

The definitive version is available at http://www3.interscience.wiley.co