Contact information

  • e-mail
    • alba.franco@uvigo.es
  • Address
    • Departament of Statistics and O.R.
    Facultad Cc. Economicas y Empresariales
    Campus Lagoas-Marcosende
    36310 Vigo (Spain)
  • Office
    • 310
  • Phone
    • +34 986 81 3512

Alba M. Franco Pereira


Please, remember to cite this webpage whenever you use the following sources:

Band Depth and Modified Band Depth in R

  • This functions compute the Band Depth and the Modified Band Depth of Lopez-Pintado and Romo (2009) in R. The notion of depth was first considered for multivariate data to generalize order statistics, ranks, and medians to higher dimensions. Several depth definitions for multivariate data have been proposed and analyzed by Mahalanobis (1936), Tukey (1975), Oja (1983), Liu (1990), Singh (1991), Fraiman and Meloche (1999), Vardi and Zhang (2000), Koshevoy and Mosler (1997) and Zuo (2003). Direct generalization of current multivariate depths to functional data often leads to either depths that are computationally intractable or depths that do not take into account some natural properties of the functions, such as shape. For that reason several specific definitions of depth for functional data were introduces. See for example, Vardi and Zhang (2000), Fraiman and Muniz (2001), Lopez-Pintado and Romo (2005), Cuevas, Febrero and Fraiman (2007) and Lopez-Pintado and Romo (2009). The definition of depth for curves provides us with a criteria to order the sample curves from the center-outward (from the deepest to the most extreme). These functions compute the Band Depth and the Modified Band Depth of Lopez-Pintado and Romo (2009). These depths follow a graph-based approach.

    • Confidence bands for ordering percentile residual life functions in R

    • Given the advantages of the percentile residual life orders (Franco-Pereira, Lillo, Romo, and Shaked (2010)), specially in practical situations, it is convenient to develop an statistical tool to test whether two independent random samples have underlying random variables which are close with respect to a percentile residual life order or not. In the submitted work "Confidence bands for ordering percentile residual life functions", we present a nonparametric method for constructing confidence bands for the difference of two percentile residual life functions. This confidence bands provide us with evidence of whether two random variables are close with respect to a percentile residual life order or not. These bands do not only allow us to compare the whole functions, but also in a given interval. We have used the Modified Band Depth of Lopez-Pintado and Romo (2009) with J=2.