LinRegOutliers

A Julia package for outlier detection in linear regression.

Implemented Methods

• Basic diagnostics
• Hadi & Simonoff (1993)
• Kianifard & Swallow (1989)
• Sebert & Montgomery & Rollier (1998)
• Least Median of Squares
• Least Trimmed Squares
• Minimum Volume Ellipsoid (MVE)
• MVE & LTS Plot
• Billor & Chatterjee & Hadi (2006)
• Pena & Yohai (1995)
• Satman (2013)
• Satman (2015)
• Setan & Halim & Mohd (2000)
• Least Absolute Deviations (LAD)
• Least Trimmed Absolute Deviations (LTA)
• Hadi (1992)
• Marchette & Solka (2003) Data Images
• Satman's GA based LTS estimation (2012)
• Fischler & Bolles(1981) RANSAC Algorithm
• Minimum Covariance Determinant Estimator
• Summary

Unimplemented Methods

• BACON Algorithm (Billor & Hadi & Velleman (2000))
• Hadi (1994) Algorithm
• Depth based estimators (Regression depth, deepest regression, etc.)
• Theil & Sen estimator for mutliple regression

Installation

julia> ]
(@v1.5) pkg> add LinRegOutliers

or

julia> using Pgk
julia> Pkg.add("LinRegOutliers")

then

julia> using LinRegOutliers

to make all the stuff be ready!

Example

julia> using LinRegOutliers
julia> # Regression setting for Hawkins & Bradu & Kass data
julia> reg = createRegressionSetting(@formula(y ~ x1 + x2 + x3), hbk)
julia> smr98(reg)
14-element Array{Int64,1}:
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14

julia> py95(reg)["outliers"]
14-element Array{Int64,1}:
  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14

julia> reg = createRegressionSetting(@formula(calls ~ year), phones);
julia> lms(reg)
Dict{Any,Any} with 6 entries:
  "stdres"    => [2.42593, 1.62705, 0.550525, 0.584612, 0.155943, -0.272726, -0.608843, -1.03751, -0.448118, -0.228929  …  93.4182, 96.9692, 112.552, 127.209, 147.419, 174.108…
  "S"         => 1.08048
  "outliers"  => [14, 15, 16, 17, 18, 19, 20, 21]
  "objective" => 0.43276
  "coef"      => [-56.3796, 1.16317]
  "crit"      => 2.5

julia> reg = createRegressionSetting(@formula(calls ~ year), phones);

julia> lts(reg)
Dict{Any,Any} with 6 entries:
  "betas"            => [-56.5219, 1.16488]
  "S"                => 1.10918
  "hsubset"          => [11, 10, 5, 6, 23, 12, 13, 9, 24, 7, 3, 4, 8]
  "outliers"         => [14, 15, 16, 17, 18, 19, 20, 21]
  "scaled.residuals" => [2.41447, 1.63472, 0.584504, 0.61617, 0.197052, -0.222066, -0.551027, -0.970146, -0.397538, -0.185558  …  91.0312, 94.4889, 109.667, 123.943, 143.629, …
  "objective"        => 3.43133

julia> # Matrix of independent variables of Hawkins & Bradu & Kass data
julia> data = hcat(hbk.x1, hbk.x2, hbk.x3);
julia> dataimage(data)

Want to have contributions?

You are probably the right contributor

• If you have statistics background
• If you like Julia

However, the second condition is more important because an outlier detection algorithm is just an algorithm. Reading the implemented methods is enough to implement new ones. Please follow the issues. If you want to implement an algorithm which is not listed in issues, open a new issue. I am also in the Julia's Slack channel. Welcome and thank you in advance!