fastMCD algorithm in StatsBase ?

[romainFr]

Would there be interest in adding a function for minimum covariance determinant estimator (MCD), for robust covariance estimation of multivariate data ? The reference is :

Rousseeuw, P. J. and Van Driessen, K. (1999). A fast algorithm for the minimum covariance determinant estimator. Technometrics, 41, 212-223.

I wrote this simple version some time ago, it could become a PR if there's interest. If so, where would it belong, StatsBase or MultivariateStats ?

function fastMCD(X,p = ceil(Int,(sum(size(X))+1)/2);nrepeats=500)
    rng = Base.GLOBAL_RNG
    hMin = nothing
    sMin = Inf
  
    for i in 1:nrepeats
        idx = randperm(size(X,1))
        h1 = X[idx[1:p],:]    
        s0 = 0
        s1= 1
        while ((det(s1)!=det(s0)) & (det(s1)!=0))
            h0 = h1
            s0 = cov(h0)
            m = vec(mean(h0,1))
            Dis = vec(mapslices(x -> mahalanobis(x,m,inv(s0)),X,2))
            ord = sortperm(Dis)
            h1 = X[ord[1:p],:]
            s1=cov(h1)
       end
       
        if det(s1)<det(sMin)
            hMin = h1
            sMin = s1
        end
       
    end
    ## Reweighting
    sfull = cov(hMin)
    tmcd = vec(mean(hMin,1))
    dfull = vec(mapslices(x -> mahalanobis(x,tmcd,inv(sfull)),hMin,2))
    smcd = (median(dfull.^2)/pdf(Chisq(size(X,2)),0.5))*sfull
    dmcd = vec(mapslices(x -> mahalanobis(x,tmcd,inv(smcd)),hMin,2));
    w = FrequencyWeights(((dmcd.^2).<pdf(Chisq(size(X,2)),0.975))*1)
    t1 = mean(hMin,w,1)
    s1 = cov(hMin,w,corrected=true)
    (t1,s1)
end

[andreasnoack]

Would be great to get but it should probably go into MultivariateStats since this package should mainly contain common and typically a bit old-fashioned algorithms.