MFHD (version 0.0.1)

MFHD: Multivariate functional halfspace depth and median for two-dimensional functional data.

Description

MFHD calculates the MFHD depth and MFHD median for two-dimensional functional data. Additionally MFHD computes for every curve at every time point whether or not it is outlying, based on the bivariate bagplot.

Usage

MFHD(y1,y2,alpha=0.125,Beta=0.5,Time=NULL)

Arguments

y1

first set of n functional curves, matrix with T columns.

y2

second set of curves (in particular, y2 can be the derivative of y1).

alpha

the level of the depth regions used for the computation of the weights: This value should be smaller than the maximal halfspace depth at any time point, divided by n. Default is 0.125. alpha=NULL defaults to uniform weights for all cross-sections.

Beta

beta-value for the dispersion curve. Should be between 0 and 1. Default is 0.50.

Time

If the measurements are not equidistant, a sorted numeric vector containing a set of time points. Default to NULL in which case it is ignored.

Value

A list with the following components:

MFHDdepth

n-vector containing the MFHD depth of every curve.

MFHDmedian

2 by T-vector of MFHD median.

weights

T-vector of MFHD weights (used in the definition of the MFHD depth).

disp

(2xT)-vector of dispersion curves (of level Beta) for y1 and y2.

loc.outl

n by T matrix of flags (takes value 1 if curve i is outlying at time point j).

References

Claeskens, G., Hubert, M., Slaets, L. and Vakili, K. (2013) "Multivariate Functional Halfspace Depth", Journal of the American Statistical Association, in press.

Examples

set.seed(123)
n<-30;
T<-60;
t.<-seq(0,2*pi,l=T)
y1<-matrix(NA,n,T)
for(i in 1:n) y1[i,]<-loess((1/2*sin(t.)+3/2*cos(t.)+rnorm(T))~I(1:T),span=1/4)$fitted
y2<-derivcurves(y1)
results<-MFHD(y1=y1,y2=y2,alpha=0.125,Beta=0.5)