fda.usc (version 1.2.3)

Depth for univariate fdata: Provides the depth measure for functional data

Description

Compute measure of centrality of the functional data. Type of depth function: Fraiman and Muniz (FM) depth, modal depth, random tukey (RT), random project (RP) depth and double random project depth (RPD).

• depth.FM computes the integration of an univariate depth along the axis x (see Fraiman and Muniz 2001). It is also known as Integrated Depth.

• depth.mode implements the modal depth (see Cuevas et al 2007).

• depth.RT implements the Random Tukey depth (see Cuesta--Albertos and Nieto--Reyes 2008).

• depth.RP computes the Random Projection depth (see Cuevas et al. 2007).

• depth.RPD implements a depth measure based on random projections possibly using several derivatives (see Cuevas et al. 2007).

• depth.FSD computes the Functional Spatial Depth (see Sguera et al. 2014).

• depth.KFSD implements the Kernelized Functional Spatial Depth (see Sguera et al. 2014).

Usage

depth.FM(fdataobj,fdataori=fdataobj,trim=0.25,scale=FALSE,
dfunc="FM1",par.dfunc = list(scale = TRUE), draw = FALSE)
depth.mode(fdataobj,fdataori=fdataobj,trim=0.25,
metric=metric.lp,h=NULL,scale=FALSE,draw=FALSE,...)
depth.RT(fdataobj,fdataori=fdataobj, trim = 0.25, nproj = 10, 
proj = 1, xeps = 1e-07, draw = FALSE, ...)
depth.RP(fdataobj,fdataori=fdataobj,trim=0.25,nproj=50,
proj="vexponential",dfunc="TD1",par.dfunc=list(),scale=FALSE,
draw=FALSE,...)
depth.RPD(fdataobj,fdataori=fdataobj,nproj=50,proj=1,deriv=c(0,1),
trim=0.25,dfunc2=depth.mode,method="fmm",draw=FALSE,...)  
depth.FSD(fdataobj, fdataori = fdataobj,  trim = 0.25, scale = FALSE, draw = FALSE) 
depth.KFSD(fdataobj, fdataori = fdataobj, trim = 0.25, h=NULL,scale = FALSE, 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.

trim

The alpha of the trimming.

nproj

The number of projections.

proj

matrix or fdata class object with a random projection provided by the user. If is a character: create the random projection using a covariance matrix by process indicated in the argument. Otherwise, it is a sigma parameter of rproc2fdata function.

dfunc

type of univariate depth function used inside depth function: "FM1" refers to the original Fraiman and Muniz univariate depth (default), "TD1" Tukey (Halfspace),"Liu1" for simplical depth, "LD1" for Likelihood depth and "MhD1" for Mahalanobis 1D depth. Also, any user function fulfilling the following pattern FUN.USER(x,xx,...) and returning a dep component can be included.

par.dfunc

List of parameters for dfunc.

dfunc2

Second depth function in RPD depth, by default depth.mode.

deriv

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

method

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

h

Bandwidth parameter.

1. If h is a numerical value, the procedure considers the argument value as bandwidth.
2. If is NULL (by default) the bandwidth is provided as the 15%--quantile of the distance between fdataobj and fdataori.
3. If h is a character string (like "q-0.15"), the procedure reads the numeric value from the third position of the character to the end and uses it to compute the quantile of the distance between fdataobj and fdataori (as in the second case).

metric

Metric function, by default metric.lp. Distance matrix between fdataobj and fdataori.

scale

=TRUE, scale the depth.

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 from the (1-trim)% deepest curves.

ltrim

Indexes of curves that conform the trimmed mean mtrim.

dep

Depth of each curve of fdataobj w.r.t. fdataori.

dep.ori

Depth of each curve of fdataori w.r.t. fdataori.

proj

The projection value of each point on the curves.

dist

Distance matrix between curves or functional data.

Details

• The modal depth depth.mode function calculates the depth of a datum accounting the number of curves in its neighbourhood. By default, the distance is calculated using metric.lp function although any other distance could be employed through argument metric (with the general pattern USER.DIST(fdataobj,fdataori)).

• The depth.RP function summarizes the random projections through averages whereas the depth.RT function uses the minimum of all projections.
• The depth.RPD function involves the original trajectories and the derivatives of each curve in two steps. It builds random projections for the function and their derivatives (indicated in the parameter deriv) and then applies a depth function (by default depth.mode) to this set of random projections (by default the Tukey one).

• The depth.FSD and depth.KFSD are the implementations of the default versions of the functional spatial depths proposed in Sguera et al 2014. At this moment, it is not possible to change the kernel in the second one.

References

Cuevas, A., Febrero-Bande, M., Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics 22, 3, 481-496.

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

Cuesta--Albertos, JA, Nieto--Reyes, A. (2008) The Random Tukey Depth. Computational Statistics and Data Analysis Vol. 52, Issue 11, 4979-4988.

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/

Sguera C, Galeano P, Lillo R (2014). Spatial depth based classification for functional data. TEST 23(4):725--750.

See Also

See Also as Descriptive.

Examples

## Not run: 
# #Ex: CanadianWeather data
# tt=1:365
# fdataobj<-fdata(t(CanadianWeather$dailyAv[,,1]),tt)
# # Fraiman-Muniz Depth
# out.FM=depth.FM(fdataobj,trim=0.1,draw=TRUE)
# #Modal Depth
# out.mode=depth.mode(fdataobj,trim=0.1,draw=TRUE)
# out.RP=depth.RP(fdataobj,trim=0.1,draw=TRUE)
# out.RT=depth.RT(fdataobj,trim=0.1,draw=TRUE)
# out.FSD=depth.FSD(fdataobj,trim=0.1,draw=TRUE)
# out.KFSD=depth.KFSD(fdataobj,trim=0.1,draw=TRUE)
# ## Double Random Projections
# out.RPD=depth.RPD(fdataobj,deriv=c(0,1),dfunc2=depth.FM,
# trim=0.1,draw=TRUE)
# out<-c(out.FM$mtrim,out.mode$mtrim,out.RP$mtrim,out.RPD$mtrim)
# plot(fdataobj,col="grey")
# lines(out)
# cdep<-cbind(out.FM$dep,out.mode$dep,out.RP$dep,out.RT$dep,out.FSD$dep,out.KFSD$dep)
# colnames(cdep)<-c("FM","mode","RP","RT","FSD","KFSD")
# pairs(cdep)
# round(cor(cdep),2)
# ## End(Not run)