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depthR

Multivariate depth functions for general dimension.

depthR provides efficient, general-purpose implementations of statistical depth functions in arbitrary dimension d. The goal is to make depth-based inference — robust location, outlier detection, multivariate ranks, depth-based quantile regions — actually usable by any R user, at any reasonable d and n.

Existing R packages for depth (ddalpha, depth, DepthProc) cap out at low dimension or are too slow for practical use at large d. depthR uses C++ backends via RcppEigen and RcppParallel to remove that barrier.

Depth Functions

Function	Notes
`mahalanobis_depth()`	Baseline; deepest point is the mean
`tukey_depth()`	Halfspace depth; adaptive random projection approximation
`simplicial_depth()`	Liu (1990); adaptive Monte Carlo with Bernoulli stopping rule
`projection_depth()`	Stahel-Donoho outlyingness; robust and affine invariant
`spatial_depth()`	Closed-form estimate; fastest option for large n and d

Installation

# From CRAN
install.packages("depthR")

# Development version
devtools::install_github("penny4nonsense/depthR")

Quick Start

library(depthR)
set.seed(42)
data <- matrix(rnorm(1000), nrow = 200, ncol = 5)

# Compute depth once — derive everything else cheaply
dd <- compute_depth(data, depth_fn = simplicial_depth)

# Depth-based median — robust multivariate location estimate
median(dd)

# Depth-based ranks — rank 1 is the deepest point
head(rank(dd))

# Outlier detection — bottom 5% by depth
outliers(dd, threshold = 0.05)

# Central region — inner 50% of data
central_region(dd, alpha = 0.50)

# Plot — outliers flagged in red
plot(dd)

DD-Plot

The depth-depth plot is the multivariate analog of the QQ-plot, useful for two-sample comparison:

x <- matrix(rnorm(400), nrow = 200, ncol = 2)
y <- matrix(rnorm(400, mean = 2), nrow = 200, ncol = 2)
dd_plot(x, y, depth_fn = tukey_depth)

References

Liu, R. Y. (1990). On a notion of data depth based on random simplices. Annals of Statistics, 18(1), 405–414.
Vardi, Y. & Zhang, C.-H. (2000). The multivariate L1-median and associated data depth. PNAS, 97(4), 1423–1426.
Zuo, Y. & Serfling, R. (2000). General notions of statistical depth function. Annals of Statistics, 28(2), 461–482.
Serfling, R. (2006). Depth functions in nonparametric multivariate inference. DIMACS Series in Discrete Mathematics, 72, 1–16.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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