# A brief introduction to STARRS

#### Daphné Giorgi, Antoine Godichon-Baggioni, Stéphane Robin

# 1 Introduction

STARRS is a comprehensive package for STochastic Algorithms for Robust multivaRiate Statistics. Robustness is a key aspect in statistical analysis, especially when dealing with real-world data that may contain outliers or be subject to various types of noise. STARRS provides a suite of tools and algorithms designed to enhance the robustness of multivariate statistical methods, replacing the use of traditional covariance matrices with more robust alternatives. The package includes implementations of several stochastic algorithms for the most common robust multivariate statistics, such as:

- Robust Median and Median Covariance Matrix Estimation
- Robust Outlier Detection Methods
- Robust Clustering Algorithms
- Robust Regression Techniques

# 2 First steps with STARRS

To get started with STARRS, you can install the package from CRAN using the following command:

    install.packages("STARRS")

Once installed, you can load the package into your R session

    library(STARRS)

The basic functions in the STARRS package are the computation of median and the median covariance matrix. These computations have several implementations, based on different algorithms, performed using Online, Offline or Semi-Online approaches. Here is an example of how to compute the median and median covariance matrix using the `STARRS` package:

    # Load the STARRS package
    library(STARRS)
    # Generate some example data
    data <- rSphereGM(n=500,d=5,K=3)

    # Compute the median using the Weiszfeld algorithm
    median_est <- WeiszfeldMedian(data$X)
    print(median_est)
    #>           [,1]      [,2]      [,3]      [,4]     [,5]
    #> [1,] -3.091029 0.8289249 -1.791928 0.7352348 -1.48842

    # Compute the median covariance matrix
    medianCov <- WeiszfeldMedianCovariance(data$X,median_est=median_est)
    print(medianCov)
    #>             [,1]       [,2]        [,3]       [,4]       [,5]
    #> [1,]  1.73683853 -0.8026144  0.05780958  0.7713579 -1.1869391
    #> [2,] -0.80261439  1.6176385  0.16626145 -1.0306765  0.7072443
    #> [3,]  0.05780958  0.1662615  1.31083896 -0.5700337 -1.0024330
    #> [4,]  0.77135786 -1.0306765 -0.57003372  2.4663104  0.1583683
    #> [5,] -1.18693914  0.7072443 -1.00243303  0.1583683  4.1772426