Multivariate Outlier Detection With High-Breakdown Estimators

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Influence functions of the Spearman and Kendall correlation measures (2010, methodology): “(iii) From (9) and (14), we obtain ASV(R̃K ,Φρ) = π2(1−ρ2)EΦρ [ ( 2PΦρ [(X−X1)(Y −Y1) > 0]−1− 2 π arcsin(ρ) )2 ] which can be rewritten as ASV(R̃K ,Φρ) = cE[(K(X ,Y )−E[K(X ,Y )])2] = c{E[K2(X ,Y )]−ρ2K}, (22) where K(x,y) = 2PΦρ [(X−x)(Y −y) > 0]−1 = 1−2(Φ(x)+Φ(y))+4Φρ(x,y) and c = π2(1−ρ2).”
Outlier detection for high-dimensional data (2015, methodology): “Along similar lines, Cerioli (2010) developed a multivariate outlier test, which performs well in terms of both size and power.”