fda.usc (version 0.9.4)

depth.RP: Provides the depth measure using random projections for functional data

Description

The depth.RP function implements a depth measure based on random projections.

Usage

depth.RP(fdataobj,trim=0.25,nproj=50,xeps=0.0000001,draw=FALSE,...)

Arguments

fdataobj

fdata class object.

trim

The alpha of the trimming.

nproj

The number projection.

xeps

Accuracy. The left limit of the empirical distribution function.

draw

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

...

Further arguments passed to or from other methods.

Value

• median
  Deepest curve.
• lmed
  Index deepest element median.
• mtrim
  code{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.
• proj
  The projection value of each point on the curves.

Details

It builds random projections and calculates the functional depth by the Tukey method combining the information of all projections..

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.

See Also

See Also as depth.RPD, depth.FM or depth.mode.

Examples

#Ex: CanadianWeather data
fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]))

# Random Projections
t=1:365
out.RP=depth.RP(fdataobj,draw=TRUE)
out.RP2=depth.RP(fdataobj,trim=0.1,draw=TRUE)
out.RP3=depth.RP(fdataobj,nproj=5,draw=TRUE)
out.RP4=depth.RP(fdataobj,nproj=30,draw=TRUE)
plot(out.RP$mtrim,type="l",lwd=2)
lines(out.RP2$mtrim,col=2,lwd=2,lty=2)
lines(out.RP3$mtrim,col=3,lwd=2,lty=3)
lines(out.RP4$mtrim,col=4,lwd=2,lty=4)