fda.usc (version 0.9.4)

depth.FM: Fraiman-Muniz depth measure

Description

The Fraiman and Muniz (FM) depth.

Usage

depth.FM(fdataobj,trim=0.25,xeps=0.00000001,draw=FALSE,...)

Arguments

fdataobj

fdata class object.

trim

The alpha of the trimming.

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
  fdata class object with the average of the (1-trim)% deepest curves.
• ltrim
  Index of curves with trimmed mean mtrim.
• dep
  Depth of each curve.

Details

Depth.FM measures the conditional quantile on all points and then integrated. The depth.FM method sorts the depths along the axis x, ie, performs a ranking of depths.

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, 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. Fraiman R, Muniz G. (2001). Trimmed means for functional data. Test 10: 419{-}440.

See Also

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

Examples

#Ex: CanadianWeather data
t=1:365
fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]),t)

# Fraiman-Muniz Depth
out.FM=depth.FM(fdataobj,draw=TRUE)
out.FM2=depth.FM(fdataobj,trim=0.1,draw=TRUE)
plot(out.FM$mtrim,type="l",lwd=2)
lines(out.FM2$mtrim,col=2,lwd=2,lty=2)