Statistical Depth Functions for Multivariate Analysis

Data depth concept offers a variety of powerful and user friendly tools for robust exploration and inference for multivariate data. The offered techniques may be successfully used in cases of lack of our knowledge on parametric models generating data due to their nature. The package consist of among others implementations of several data depth techniques involving multivariate quantile-quantile plots, multivariate scatter estimators, multivariate Wilcoxon tests and robust regressions.

DepthProc project consist of a set of statistical procedures based on so called statistical depth functions. The project involves free available R package and its description.

Versions

CRAN release version

Installation

DepthProc is avaiable on CRAN:

install.packages("DepthProc")

You can also install it from GitHub with devtools package:

library(devtools)
install_github("zzawadz/DepthProc")

Main features:

Speed and multithreading

Most of the code is written in C++ for additional efficiency. We also use OpenMP to speedup computations with multithreading:

library(DepthProc)
set.seed(123)
 
d <- 10
x <- mvrnorm(1000, rep(0, d), diag(d))
# Default - utilize as many threads as possible
system.time(depth(x, x, method = "LP"))
#>    user  system elapsed 
#>   0.351   0.000   0.090
 
# Only single thread - 4 times slower:
system.time(depth(x, x, method = "LP", threads = 1))
#>    user  system elapsed 
#>   0.208   0.000   0.208
 
# Two threads - 2 times slower:
system.time(depth(x, x, method = "LP", threads = 2))
#>    user  system elapsed 
#>   0.201   0.000   0.103

Available depth functions

x <- mvrnorm(100, c(0, 0), diag(2))
 
depthEuclid(x, x)
depthMah(x, x)
depthLP(x, x)
depthProjection(x, x)
depthLocal(x, x)
depthTukey(x, x)
 
## Base function to call others:
depth(x, x, method = "Projection")
depth(x, x, method = "Local", depth_params1 = list(method = "LP"))
 
## Get median
depthMedian(x, 
  depth_params = list(
    method = "Local",
    depth_params1 = list(method = "LP")))

Basic plots

Contour plot

library(mvtnorm)
y <- rmvt(n = 200, sigma = diag(2), df = 4, delta = c(3, 5))
depthContour(y, points = TRUE, graph_params = list(lwd = 2))

Perspective plot

depthPersp(y, depth_params = list(method = "Mahalanobis"))

Functional depths:

There are two functional depths implemented - modified band depth (MBD), and Frainman-Muniz depth (FM):

x <- matrix(rnorm(60), nc = 20)
fncDepth(x, method = "MBD")
fncDepth(x, method = "FM", dep1d = "Mahalanobis")
#> Warning in dep1d_params$u <- u[, i]: Coercing LHS to a list

Functional BoxPlot

x <- matrix(rnorm(2000), ncol = 100)
fncBoxPlot(x, bands = c(0, 0.5, 1), method = "FM")