The h-mode depth of functional real-valued data.
depthf.hM(datafA, datafB, range = NULL, d = 101, norm = c("C", "L2"),
q = 0.2)A vector of length m of the h-mode depth values.
Functions whose depth is computed, represented by a dataf object of their arguments
and functional values. m stands for the number of functions.
Random sample functions with respect to which the depth of datafA is computed.
datafB is represented by a dataf object of their arguments
and functional values. n is the sample size. The grid of observation points for the
functions datafA and datafB may not be the same.
The common range of the domain where the functions datafA and datafB are observed.
Vector of length 2 with the left and the right end of the interval. Must contain all arguments given in
datafA and datafB.
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 d
corresponding to equi-spaced points in the domain given by the interval range. Functional values in these
points are reconstructed using linear interpolation, and extrapolation.
The norm used for the computation of the depth. Two possible
choices are implemented: C for the uniform norm of continuous functions,
and L2 for the \(L^2\) norm of integrable functions.
The quantile used to determine the value of the bandwidth \(h\)
in the computation of the h-mode depth. \(h\) is taken as the q-quantile of
all non-zero distances between the functions B. By default, this value is set
to q=0.2, in accordance with the choice of Cuevas et al. (2007).
Stanislav Nagy, nagy@karlin.mff.cuni.cz
The function returns the vectors of the sample h-mode depth values. The kernel used in the evaluation is the standard Gaussian kernel, the bandwidth value is chosen as a quantile of the non-zero distances between the random sample curves.
Cuevas, A., Febrero, M. and Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics 22 (3), 481--496.
Nagy, S., Gijbels, I. and Hlubinka, D. (2016). Weak convergence of discretely observed functional data with applications. Journal of Multivariate Analysis, 146, 46--62.
datafA = dataf.population()$dataf[1:20]
datafB = dataf.population()$dataf[21:50]
depthf.hM(datafA,datafB)
depthf.hM(datafA,datafB,norm="L2")
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