Robustbase

The package Robustbase provides "Essential" Robust Statistics - tools allowing to analyze data with robust methods: univariate methods, multivariate statistics and regression. We strive to cover the book "Robust Statistics, Theory and Methods (with R)" by 'Maronna, Martin, Yohai and Salibian-Barrera'; Wiley 2019. The package is based on the R packages robustbase and rrcov.

Installation

The package Robustbase can be installed using the Julia REPL as follows

julia> ]
(@v1.12) pkg> add Robustbase

or

julia> using Pkg
julia> Pkg.add("Robustbase")

and then

julia> using Robustbase

to make it available to the user.

Documentation

Please check out the reference manual here.

Functionalities

1. Univariate statistics

The univariate module contains several univariate location and scale estimators. They all implement the abstract base class RobustScale, which has the properties location and scale and can be fitted using the fit! method. Each class is expected to implement a _calculate method where the attributes scale_ and location_ are set. All functions have matrix versions which can be called on a matrix or a data frame specifying the required dimension on which to do the calculations.

Example

Let's have the following 10 observations. The classical methods for estimating the parameters of the model, the arithmetic mean and standard deviation, may be affected by outliers.

x = [9.52, 9.68, 10.16, 9.96, 10.08, 9.99, 10.47, 9.91, 9.92, 15.21]
mean(x)
std(x)

Estimator	All 10 observations	Only 9 regular observations
$\bar x_n$	10.49	9.97
$median$	9.98	9.96
$\tau-location$	9.96	9.96
$Stdev_n$	1.68	0.27
$IQRN$	0.17	0.13
$MAD$	0.21	0.18
$\tau-scale$	0.28	0.22
$Q_n-scale$	0.37	0.31

2. Covariance

Similarly as in the univariate case outliers can influence the estimators of multivariate data, these are in first line the multivariate location and covariance esimators. Apart from being useful for outlier detection through computing the Mahalanobis distances, they are cornerstones of many other multivariate methods like principal component analysis and discriminant analysis. The most popular robust estimator of multivariate location and covariance is the Minimum Covariance Determinant (MCD) estimator of Rousseeuw (1084) which is widely used after the fast algorithm of Rousseeuw and van Driessen (1999) became available. A faster version of the MCD is the deterministic MCD of Hubert, Rousseeuw and Verdonck (2012) which instead of doing time consuming resampling starts from six rough robust estimators which are easy to compute.

The covariance module implements curently three frequently used scatter estimators: The Fast MCD, the deterministic MCD and the OGK. They all use the new abstract base class RobustCovariance which extends the CovarianceEstimator class from StatsBase. The RobustCovariance class includes the distance-distance plot. It shows the robust distances versus the classical Mahalanobis distances, and is equipped with thresholds for outlier detection. The plot is drawn by the dd_plot() function function, after obtaining a robust covariance estimator by the fit!() method.

Example

mcd = CovMcd();
fit!(mcd, hbk[:, 1:3]);
display(mcd)
dd_plot(mcd)

-> Method:  Fast MCD Estimator: (alpha=0.5 ==> h=39)

Robust estimate of location:
[1.55833, 1.80333, 1.66]

Robust estimate of covariance:
3×3 Matrix{Float64}:
 1.21312    0.0239154  0.165793
 0.0239154  1.22836    0.195735
 0.165793   0.195735   1.12535

3. Data sets

Robustbase includes several datasets that are often used in the robustness literature. These datasets serve as standard examples and benchmarks, allowing users to easily test robust algorithms. They are also available in the R-packages robustbase and rrcov.

4. Further development

• Add S- and MM-estimators of multivariate location and covariance matrix
• Add regression analysis: Least Trimmed Squares regression
• Add Principal component analysis
• Add Discriminant analysis

Citation

If you use this software, please cite:

Todorov, V. (2026). "Essential" Robust Statistics. Tools to analyze data with robust methods. URL https://valentint.github.io/Robustbase.jl/stable/. doi:10.5281/zenodo.20562919

or in BibTeX format:

@software{Robustbase.jl,
    author = {Valentin Todorov},
    doi = {10.5281/zenodo.20562919},
    license = {["MIT"]},
    title = {{"Essential" Robust Statistics. Tools to analyze data with robust methods.}},
    year = 2026,
    url = {https://valentint.github.io/Robustbase.jl/stable/}}

Community guidelines

Report issues and request features

If you experience any bugs or issues or if you have any suggestions for additional features, please submit an issue via the Issues tab of this repository. Please have a look at existing issues first to see if your problem or feature request has already been discussed.

Contribute to the package

If you want to contribute to the package, you can fork this repository and create a pull request after implementing the desired functionality.

Ask for help

If you need help using the package, or if you are interested in collaborations related to this project, please get in touch with the package maintainer.