initial implementation of the robust hat matrix based robust regression estimator

Author: jbytecode

CHANGELOG.md

@@ -1,5 +1,6 @@
 # v0.11.5 (Upcoming Release)
 
+- Initial implementation of the robust hat matrix regression estimator
 
 # v0.11.4 
 

src/LinRegOutliers.jl

@@ -212,6 +212,10 @@ import .TheilSen: theilsen
 include("deepestregression.jl")
 import .DeepestRegression: deepestregression
 
+# Robust Hat matrix based regression 
+include("robhatreg.jl")
+import .RobustHatRegression: robhatreg
+
 # All-in-one
 include("summary.jl")
 import .Summary: detectOutliers
@@ -275,10 +279,11 @@ export bacon
 export cm97
 export theilsen
 export deepestregression
+export robhatreg
 
 
 # Snoop-Precompile 
-include("precompile/precompile.jl")
+# include("precompile/precompile.jl")
 
 
 end # module

src/robhatreg.jl

@@ -0,0 +1,107 @@
+module RobustHatRegression 
+
+
+export robhatreg
+
+import ..Basis: RegressionSetting, @extractRegressionSetting, designMatrix, responseVector
+import ..OrdinaryLeastSquares: ols, residuals, coef
+import ..LTS: iterateCSteps
+
+import Distributions: quantile 
+import LinearAlgebra: inv, diag
+
+
+function trimean(u::AbstractVector{T})::Float64 where T <: Real
+    return (quantile(u, 0.25) + 2.0 * quantile(u, 0.50) + quantile(u, 0.75)) / 4.0
+end
+
+function m(v::Vector, u::Vector)::Float64
+    return trimean(u .* v) * length(u)
+end
+
+function m(mat::AbstractMatrix, u::AbstractVector)::AbstractMatrix
+    L = length(u)
+    y = zeros(Float64, L, 1)
+    for i in 1:L
+        y[i, 1] = u[i]
+    end
+    result =  m(mat, y)
+    return result
+end
+
+function m(m1::AbstractMatrix, m2::AbstractMatrix)
+    n1, _ = size(m1)
+    _ , p2 = size(m2)
+    newmat = zeros(Float64, n1, p2)
+    for i in 1:n1
+        for j in 1:p2
+            newmat[i, j] = m(m1[i, :], m2[:, j])
+        end
+    end
+    return newmat
+end
+
+function hatrob(x::AbstractMatrix)
+    return x * inv(m(x', x)) * x'
+end
+
+
+"""
+    robhatreg(setting::RegressionSetting)
+
+Perform robust regression using the robust hat matrix method.
+
+# Arguments
+- `setting::RegressionSetting`: The regression setting.
+
+# Returns
+
+- A dictionary containing the following
+    - `betas::AbstractVector`: The estimated coefficients.
+
+# References
+
+Satman, Mehmet Hakan, A robust initial basic subset selection 
+method for outlier detection algorithms in linear regression, In Press
+"""
+function robhatreg(setting::RegressionSetting)
+    X, y = @extractRegressionSetting setting
+    return robhatreg(X, y)
+end
+
+
+"""
+    robhatreg(X, y)
+
+Perform robust regression using the robust hat matrix method.
+
+# Arguments
+
+- `X::AbstractMatrix`: The design matrix.
+- `y::AbstractVector`: The response vector.
+
+# Returns
+
+- A dictionary containing the following
+    - `betas::AbstractVector`: The estimated coefficients.
+
+# References
+
+Satman, Mehmet Hakan, A robust initial basic subset selection 
+method for outlier detection algorithms in linear regression, In Press
+"""
+function robhatreg(X, y)
+    n, p = size(X)
+    h = Int(ceil((n + p + 1)/2))
+    myhat = hatrob(X)
+    diagonals = diag(myhat)
+    prms = sortperm(diagonals)
+    bestindices = prms[1:(p+1)]
+    _, indices = iterateCSteps(X, y, bestindices, h)
+    betas = X[indices, :] \ y[indices]
+    return Dict("betas" => betas)
+end
+
+
+
+end # end of module RobustHatRegression

test/runtests.jl

@@ -36,4 +36,5 @@ include("testbacon2000.jl")
 include("testdataimage.jl")
 include("testtheilsen.jl")
 include("testsummary.jl")
-include("testdeepestregression.jl")
+include("testdeepestregression.jl")
+include("testrobhatreg.jl")

test/testrobhatreg.jl

@@ -0,0 +1,34 @@
+
+
+@testset "Robust Hat Matrix based Robust Regression" begin
+    # Create simple data
+    rng = MersenneTwister(12345)
+    n = 50
+    x = collect(1:n)
+    e = randn(rng, n) .* 2.0
+    y = 5 .+ 5 .* x .+ e
+
+    # Contaminate some values 
+    y[n] = y[n] * 2.0
+    y[n-1] = y[n-1] * 2.0
+    y[n-2] = y[n-2] * 2.0
+    y[n-3] = y[n-3] * 2.0
+    y[n-4] = y[n-4] * 2.0
+
+    df = DataFrame(x=x, y=y)
+
+    reg = createRegressionSetting(@formula(y ~ x), df)
+    result = robhatreg(reg)
+
+    betas = result["betas"]
+
+    atol = 1.0
+
+    @test isapprox(betas[1], 5.0, atol=atol)
+    @test isapprox(betas[2], 5.0, atol=atol)
+end
+
+
+
+
+