fda.usc (version 1.0.0)

depth.RPD: Provides the depth measure by random projections using derivatives

Description

The depth.RPD function implements a depth measure based on random projections and using several derivatives.

Usage

depth.RPD(fdataobj,fdataori=fdataobj,nproj=50,proj=1,deriv=c(0,1),trim=0.25,
dfunc2=depth.mode,method="fmm",draw=FALSE,...)

Arguments

fdataobj

A set of new curves to evaluate the depth. fdata class object.

fdataori

A set of original curves where the depth is computed. fdata class object.

nproj

Number of random projection.

deriv

Number of derivatives described in integer vector deriv. =0 means no derivative.

proj

if is a character: create the random projection using a covariance matrix by process indicated in the argument (by default, proj=1, sigma=diag(ncol(fdataobj))), else if is a matrix of random projection provided by the user.

trim

The alpha of the trimming.

dfunc2

by default, depth.mode.

method

Type of derivative method. See fdata.deriv for more details.

draw

=TRUE, draw the curves, the sample median and the trimmed mean.

...

Further arguments passed to or from other methods.

Value

• median
  Deepest curve.
• lmed
  Index deepest element median.
• mtrim
  fdata class object with the average from the (1-trim)% deepest curves.
• ltrim
  Index of curves with trimmed mean mtrim.
• dep
  Depth of each curve.
• dep
  Depth of each curve.
• proj
  The projection value of each point on the curves.

Details

Calculate the depth in two steps. It builds random projections for the funcion and their derivatives (indicated in the parameter deriv) without looking at the functional data . Then it applyes a depth function (by default depth.mode) to the set of random projections created for calculate the functional depth by the Tukey method.

References

Cuevas, A., Febrero-Bande, M. and Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics 22, 3, 481{-}496. Febrero-Bande, M., Galeano, P., and Gonzalez-Manteiga, W. (2008). Outlier detection in functional data by depth measures with application to identify abnormal NOx levels. Environmetrics 19, 4, 331{-}345. J. A. Cuesta-Albertos, R. Fraiman and T. Ransford. Random projections and goodness-of-fit tests in infinite-dimensional spaces. Boletim da Sociedade Brasileira de Matematica (2006), 37(4), 1{-}25. Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

See Also

See Also as depth.RP, depth.FM and depth.mode.

Examples

## Not run
## Double Random Projections in CanadianWeather data
 
# fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]))
# t=1:365
# out.RPD=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=depth.RP,draw=TRUE)
# out.RPD2=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=depth.mode,draw=TRUE,
# method="fmm")
# out.RPD3=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=depth.FM,draw=TRUE,
# method="fmm")

# plot(out.RPD$mtrim,type="l",lwd=2)
# lines(out.RPD2$mtrim,col=2,lwd=2,lty=2)
# lines(out.RPD3$mtrim,col=3,lwd=2,lty=3)