Barale - Shirke Test

R implementation of two samples location/scale multidimensional test proposed by (Barale, 2020).

About the code

The test is performed by the function called baraleShirkeTest. This function is defined in baraleShirke.cpp. That files contains several functions that are used in the baraleShirkeTest function. baraleShirke.R contains the function baraleShirke.test which is the function that the user shoud call.

Dependencies

The test is implemented in C++ in order to aproximate the p-value with a higher precision at a lower cost. Therefore, it is necesary to install a C++ compiler, ddalpha, Rcpp and RcppArmadillo R packages, and Armadillo C++ library.

How to use it

Assuming that you have installed all the dependencies previously mentioned, you should load the function:

source("path/to/baraleShirke.R")

Now you're ready to start performing the test. You must know that the baraleshirke.test function has seven arguments that must be passed in the following order:

• X1 which is the matrix, data.frame or array that contains the observations of the first sample on its rows.

• X2 which is the matrix, data.frame or array that contains the observations of the second sample on its rows.

• depth which is a string that specifies the depth measure that is going to be used. It should be one of the following:

  • betaSkeleton
  • halfspace
  • L2
  • Mahalanobis
  • MahalanobisMCD
  • projection
  • potential
  • qhpeeling
  • simplicial
  • simplicialVolume
  • spatial
  • zonoid

• NIter which is the number of iterations that will be used to approximate the p-value.

• alpha which is significance level of the test.

• returnDepths which is a boolean that indicates if the depths should be returned.

• returnSamples which is a boolean that indicates if the resampling samples should be returned.

Arguments 3 to 7 are optional.

The function returns a list with the following entries:

• Statistic: The observed Bmax statistic.
• NIter: Number of iterations used to approximate the p-value.
• PValue: Approximated p-value.
• n1: Number of observations in sample 1.
• n2: Number of observations in sample 2.
• alpha: Significance level of the test.
• Depth: Depth measure used in the test.
• DepthVals: Computed depths (if returnDepths == TRUE). Here the first column contains the depths with respect to sample 1 and the second column, with respect to sample 2.
• Samples: Simulated statistics (if returnSamples == TRUE).
• Message: Nice message showing test output.

Files

Here you can find a list of the files that are contained on this repository:

• baraleShirke.cpp: Source code in C++.
• baraleShirke.R: baraleshirke.test function definition.
• test.r: Example code in R.
• turtles.csv: Example data (columns are separated by spaces).
• README.md: This file.

References

• M. S. Barale & D. T. Shirke (2020): A test based on data depth for testinglocation-scale of the two multivariate populations, Journal of Statistical Computation andSimulation, DOI: 10.1080/00949655.2020.1830285