POIFD

Overview

Software to compute Integrated Depth for Partially Observed Functional Data and applications

It implements the proposed depth measures, functional boxplot, functional outliergram for partially observed functional data and reconstruction methods.

Installation

#install the package
devtools::install_github("aefdz/fdaPOIFD")

#load the package
library(fdaPOIFD)

Test usage

#plot the data sets
plot_interval <- plotPOFD(exampleData$PoFDintervals)
plot_common <- plotPOFD(exampleData$PoFDextremes)

plot_interval

## Warning: Removed 2914 rows containing missing values or values outside the scale range
## (`geom_line()`).

## Warning: Removed 9900 rows containing missing values or values outside the scale range
## (`geom_point()`).

plot_common

## Warning: Removed 7368 rows containing missing values or values outside the scale range
## (`geom_line()`).

## Warning: Removed 7368 rows containing missing values or values outside the scale range
## (`geom_point()`).

Computing depths

Example with partially observed common domain. Data is in a matrix form:

mbd <- POIFD(exampleData$PoFDintervals, type = "MBD")

(median <- which.max(mbd)) # deepest curve

## 45 
## 45

• Fraiman, R. and Muniz, G. (2001). Trimmed means for functional data. Test, 10(2):419–440.
• López-Pintado, S. and Romo, J. (2009). On the concept of depth for functional data. Journal of the American Statistical Association, 104(486):718–734.
• López-Pintado, S. and Romo, J. (2011). A half-region depth for functional data. Computational Statistics and Data Analysis, 55(4):1679–1695.

Example without partially observed common domain. It implements an step to estimate the observation domain. Data is in a list form:

exampleData$PoFDintervals_list[[1]]

## $x
## [1] 0.000000000 0.005050505 0.010101010
## 
## $y
## [1] 0.7814341 0.7939221 0.8063511

To compute the POIFD, we need to include the vector where the data should be evaluated:

mbd <- POIFD(exampleData$PoFDintervals_list, type = "MBD", t = seq(0, 1, length.out = 100))

(median <- which.max(mbd)) # deepest curve

## 44 
## 44

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

Functional Boxplot and magnitude outliers

fboxplot <- boxplotPOFD(exampleData$PoFDextremes_outliers, centralRegion = 0.5, fmag = 1.5, fdom = 1)

fboxplot$magnitude

## 102 
## 102

fboxplot$domain

## 102 
## 102

fboxplot$fboxplot

## Warning: Removed 27 rows containing missing values or values outside the scale range
## (`geom_line()`).
## Removed 27 rows containing missing values or values outside the scale range
## (`geom_line()`).

• Sun, Y. and Genton, M. G. (2011). Functional boxplots. Journal of Computational and Graphical Statistics, 20(2):316–334.

Functional Outliergram and Shape Outliers

outliergram <- outliergramPOFD(exampleData$PoFDextremes_outliers)

outliergram$shape

## [1] 103 104

outliergram$outliergram

• Arribas-Gil, A. and Romo, J. (2014). Shape outlier detection and visualization for functional data: the outliergram. Biostatistics, 15(4):603–619.

Depth-based Reconstruction of Partially Observed Functional data

It implements a reconstruction method based on the partially observed functional depth and the algorithm proposed in Elías, A., Jiménez, R. and Shang, HL. (2022).

data <- exampleData$PoFDintervals
recons_data <- depthbasedreconstructionPOFD(data, id_recons = c(1:2))

par(mfrow = c(1,2))
matplot(data[,1:2], col = c("blue", "red"), type ="l", lty = 1, main = "POFD", ylab = "Y")

matplot(data[,1:2], col = c("blue", "red"), type ="l", lty = 1, main = "Reconstruction", ylab = "Y")
matplot(recons_data, col = c("blue", "red"), add = TRUE, type = "l", lty = 2, main = "Reconstruction", ylab = "Y")

par(mfrow = c(1,1))

• Elías, A., Jiménez, R. and Shang, HL. (2022) On projection methods for functional time series forecasting, Journal of Multivariate Analysis, Volume 189, 2022.

References

• Elías, A., Jiménez, R. and Shang, HL. (2022) On projection methods for functional time series forecasting, Journal of Multivariate Analysis, Volume 189, 2022.

• 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.

• Elías, A., Jiménez, R., & Shang, H. L. (2023). Depth-based reconstruction method for incomplete functional data. Computational Statistics, 38(3), 1507-1535.

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