depth.mfdata

Provides the depth measure for a list of p--functional data objects

This function computes the depth measure for a list of p--functional data objects. The procedure extends the Fraiman and Muniz (FM), modal, and random project depth functions from 1 functional dataset to p functional datasets.

Usage

depth.modep(
  mfdata,
  mfdataref = mfdata,
  h = NULL,
  metric,
  par.metric = list(),
  method = "euclidean",
  scale = FALSE,
  trim = 0.25,
  draw = FALSE,
  ask = FALSE
)
depth.RPp(
  mfdata,
  mfdataref = mfdata,
  nproj = 50,
  proj = "vexponential",
  trim = 0.25,
  dfunc = "mdepth.TD",
  par.dfunc = list(scale = TRUE),
  draw = FALSE,
  ask = FALSE
)
depth.FMp(
  mfdata,
  mfdataref = mfdata,
  trim = 0.25,
  dfunc = "mdepth.MhD",
  par.dfunc = list(scale = FALSE),
  draw = FALSE,
  ask = FALSE,
  ...
)

Details

• depth.FMp, this procedure suposes that each curve of the mfdataobj have the same support [0,T] (same argvals and rangeval). The FMp depth is defined as: \(FM_i^p =\int_{0}^{T}Z_i^p(t)dt\) where \(Z_i^p(t)\) is a \(p\)--variate depth of the vector \((x_i^1(t),\ldots,x_i^p(t))\) w.r.t. the sample at \(t\). derivatives. In this case,note solo un dato funcional se reduce depth.FM=depth.FM1

• The depth.RPp function calculates the depth in two steps. It builds random projections for the each curve of the mfdata w.r.t. each curve of the mfdataref object. Then it applyes a multivariate depth function specified in dfunc argument to the set of random projections. This procedure is a generalization of Random Projection with derivatives (RPD) implemented in depth.RPD function. Now, the procedure computes a p-variate depth with the projections using the \(p\) functional dataset.

• The modal depth depth.modep function calculates the depth in three steps. First, the function calculates a suitable metrics or semi--metrics \(m_1+\cdots+m_p\) for each curve of the mfdata w.r.t. each curve in the mfdataref object using the metric and par.metric arguments, see metric.lp or semimetric.NPFDA for more details. Second, the function uses the \(p\)--dimensional metrics to construct a new metric, specified in method argument, by default if method="euclidean", i.e. \(m:=\sqrt{m_1^2+\cdots+m_p^2}\). Finally, the empirical h--depth is computed as: $$\hat{f}_h(x_0)=N^{-1}\sum_{i=1}^{N}{K(m/h)}$$ where \(x\) is dataset with p observed fucntional data, \(m\) is a suitable metric or semi--metric, \(K(t)\) is an asymmetric kernel function and h is the bandwidth parameter.

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. 10: 419-440. 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 Descriptive.

Aliases

• depth.mfdata
• depth.modep
• depth.FMp
• depth.RPp

Examples

# NOT RUN {
data(tecator)
xx<-tecator$absorp
xx1<-fdata.deriv(xx,1)
lx<-list(xx=xx,xx=xx1)
# Fraiman-Muniz Depth
par.df<-list(scale =TRUE)
out.FM1p=depth.FMp(lx,trim=0.1,draw=TRUE, par.dfunc = par.df)
out.FM2p=depth.FMp(lx,trim=0.1,dfunc="mdepth.LD",
par.dfunc = par.df, draw=TRUE)

# Random Project Depth
out.RP1p=depth.RPp(lx,trim=0.1,dfunc="mdepth.TD",
draw=TRUE,par.dfunc = par.df)
out.RP2p=depth.RPp(lx,trim=0.1,dfunc="mdepth.LD",
draw=TRUE,par.dfunc = par.df)

#Modal Depth
out.mode1p=depth.modep(lx,trim=0.1,draw=T,scale=T)
out.mode2p=depth.modep(lx,trim=0.1,method="manhattan",
draw=T,scale=T)

par(mfrow=c(2,3))
plot(out.FM1p$dep,out.FM2p$dep)
plot(out.RP1p$dep,out.RP2p$dep)
plot(out.mode1p$dep,out.mode2p$dep)
plot(out.FM1p$dep,out.RP1p$dep)
plot(out.RP1p$dep,out.mode1p$dep)
plot(out.FM1p$dep,out.mode1p$dep)
# }
# NOT RUN {
# }