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Functional Data Depth

Source: R/depth.R
tf_depth.Rd

Data depths for functional data. All depths are scaled so that 1 means most central and 0 means most extreme. Available methods:

Usage

tf_depth(x, arg, depth = "MBD", na.rm = TRUE, ...)

# S3 method for class 'matrix'
tf_depth(
  x,
  arg,
  depth = c("MBD", "MHI", "FM", "FSD", "RPD"),
  na.rm = TRUE,
  ...
)

# S3 method for class 'tf'
tf_depth(x, arg, depth = "MBD", na.rm = TRUE, ...)

Arguments

x

tf (or a matrix of evaluations).

arg

grid of evaluation points.

depth

one of "MBD", "MHI", "FM", "FSD", or "RPD".

na.rm

remove missing observations? Defaults to TRUE.

...

for "RPD": u (regularization quantile, default 0.01), n_projections (M, default 5000), n_projections_beta (L, default 500).

Value

vector of depth values

Details

  • "MBD": Modified Band-2 Depth (default). Scale of 0 (most extreme) to 1 (most central).

  • "MHI": Modified Hypograph Index. Ranks functions from lowest (0) to highest (1) instead of most extreme to most central! For functions that never cross: \(MBD = -2(MHI - 0.5)^2 + .5\).

  • "FM": Fraiman-Muniz depth. Integrates pointwise univariate halfspace depths over the domain. Scale of 0 (most extreme) to 1 (most central).

  • "FSD": Functional Spatial Depth. Based on spatial signs; robust to outliers. Scale of 0 (most extreme) to 1 (most central).

  • "RPD": Regularized Projection Depth. Projects curves onto random directions and computes outlyingness. Especially useful for detecting shape outliers. Scale of 0 (most extreme) to 1 (most central). Note: results depend on the RNG state; set a seed (e.g. set.seed(...)) before calling for reproducibility. Accepts additional arguments via ...: u (quantile level for regularization, default 0.01), n_projections (M, number of projection directions, default 5000), n_projections_beta (L, directions for estimating regularization parameter, default 500).

References

Sun, Ying, Genton, G M, Nychka, W D (2012). “Exact fast computation of band depth for large functional datasets: How quickly can one million curves be ranked?” Stat, 1(1), 68–74.

López-Pintado, Sara, Romo, Juan (2009). “On the concept of depth for functional data.” Journal of the American Statistical Association, 104(486), 718–734.

López-Pintado, Sara, Romo, Juan (2011). “A half-region depth for functional data.” Computational Statistics & Data Analysis, 55(4), 1679–1695.

Fraiman, Ricardo, Muniz, Graciela (2001). “Trimmed means for functional data.” Test, 10(2), 419–440.

Chakraborty, Anirvan, Chaudhuri, Probal (2014). “The spatial distribution in infinite dimensional spaces and related quantiles and depths.” The Annals of Statistics, 42(3), 1203–1231.

Bočinec, Filip, Nagy, Stanislav, Yeon, Hyemin (2026). “Projection depth for functional data: Practical issues, computation and applications.” arXiv preprint arXiv:2602.22877.

See also

Other tidyfun ordering and ranking functions: tf_minmax, tf_order

Examples

x <- tf_rgp(3)/3 + 1:3
tf_depth(x, depth = "MBD")
#> [1] 1.333333 2.000000 1.333333
tf_depth(x, depth = "MHI")
#> [1] 0.3333333 0.6666667 1.0000000
tf_depth(x, depth = "FM")
#> [1] 0.6666667 0.6666667 0.0000000
tf_depth(x, depth = "FSD")
#> [1] 0.3335162 0.9426997 0.3346406