fdaPOIFD (version 2.0.0)

POIFD: Integrated Depth for Partially Observed Functional Data

Description

Compute the depth measure of a partially observed functional data set proposed in [1]. If the functions are not observed in a common partially observed domain, the code first estimates the observation domain using the proposal in [2].

Usage

POIFD(data, type = c("HD", "FMD", "MBD", "MHRD"), phi, t = NULL)

Value

Ordered vector of depths. The names are the functions names (if provided) or the column position.

Arguments

data

If functions are observed in a partially observed common grid `data` is a matrix `p` by `n`, being `n` the number of functions and `p` the number of grid points. The row names of the matrix should be the common evaluation grid and the column names the identifiers of each functional data. If functions do not have a common grid, `data`must be a list of length `n` where each element contains the values and evaluation points of each function. I.e. each list element must contain two vectors `x`, including the evaluation points, and `y`, the evaluated function values. For functions without a common grid, the function "POIFD") first apply the procedure to estimate the observation domain proposed in Elías, A., Nagy, S. (2025), TEST.

type

chosen depth measure. Halfspace depth ("HS"), Fraiman and Muniz depth ("FMD"), Modified band depth ("MBD") or Modified Half Region Depth and Modified Epigraph/Hipograph Index "MHRD")

phi

phi function of weights for the POIFD. The default value is as in [1]: the proportion of observed functions at each time point.

t

If functions do not have a common grid, `t` represents the final common grid of evaluation points to apply the procedure to estimate the observation domain proposed in [2].

Details

[1] Elías, A., Jiménez, R., Paganoni, A. M., & Sangalli, L. M. (2023). Integrated depths for partially observed functional data. Journal of Computational and Graphical Statistics, 32(2), 341-352.

[2] Elías, A., Nagy, S. (2025). Statistical Properties of Partially Observed Integrated Funcional Depths. TEST, 34, 125-150.

Examples

data <- exampleData$PoFDintervals
poifd <- POIFD(data,  type = c("FMD"))

data <- exampleData$PoFDintervals_list
poifd <- POIFD(data,  type = c("FMD"), t = seq(0, 1, length.out = 100))