depthf.fd1 | R Documentation |
Usual, and order extended integrated and infimal depths for real-valued functional data based on the halfspace and simplicial depth.
depthf.fd1(datafA, datafB, range = NULL, d = 101, order = 1, approx = 0)
datafA |
Functions whose depth is computed, represented by a |
datafB |
Random sample functions with respect to which the depth of |
range |
The common range of the domain where the functions |
d |
Grid size to which all the functional data are transformed. For depth computation,
all functional observations are first transformed into vectors of their functional values of length |
order |
The order of the order extended integrated and infimal depths.
By default, this is set to |
approx |
Number of approximations used in the computation of the order extended depth
for |
The function returns vectors of sample integrated and infimal depth values.
Four vectors of length m
of depth values are returned:
Simpl_FD
the integrated depth based on the simplicial depth,
Half_FD
the integrated depth based on the halfspace depth,
Simpl_ID
the infimal depth based on the simplicial depth,
Half_ID
the infimal depth based on the halfspace depth.
In addition, two vectors of length m
of the relative area of smallest depth values is returned:
Simpl_IA
the proportions of points at which the depth Simpl_ID
was attained,
Half_IA
the proportions of points at which the depth Half_ID
was attained.
The values Simpl_IA
and Half_IA
are always in the interval [0,1].
They introduce ranking also among functions having the same
infimal depth value - if two functions have the same infimal depth, the one with larger infimal area
IA
is said to be less central.
For order=2
and m=1
, two additional matrices of pointwise depths are also returned:
PSD
the matrix of size d*d
containing the computed
pointwise bivariate simplicial depths used for the computation of Simpl_FD
and Simpl_ID
,
PHD
the matrix of size d*d
containing the computed
pointwise bivariate halfspace depths used for the computation of Half_FD
and Half_ID
.
For order=3
, only Half_FD
and Half_ID
are provided.
Stanislav Nagy, nagy@karlin.mff.cuni.cz
Nagy, S., Gijbels, I. and Hlubinka, D. (2016). Weak convergence of discretely observed functional data with applications. Journal of Multivariate Analysis, 146, 46–62.
Nagy, S., Gijbels, I. and Hlubinka, D. (2017). Depth-based recognition of shape outlying functions. Journal of Computational and Graphical Statistics, 26 (4), 883–893.
depthf.fd2
, infimalRank
datafA = dataf.population()$dataf[1:20]
datafB = dataf.population()$dataf[21:50]
depthf.fd1(datafA,datafB)
depthf.fd1(datafA,datafB,order=2)
depthf.fd1(datafA,datafB,order=3,approx=51)
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