Supplementary material - Anomaly Detection in Extreme Regions via Empirical MV-sets on the Sphere
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چکیده
Throughout the proof, we assume that the marginal c.d.f. Fj , j = 1, . . . , d, are known. In other words, we analyze a surrogate of the spherical MV-set algorithm, where V̂ may be taken as V itself. Recall the definition of the finite distance angular measure Φt(A) = tP(V ∈ tCA), A ⊂ Sd−1, where CA = {tx, x ∈ A, t ≥ 1} is the truncated cone generated by A. Notice Φ(A) = limt→∞Φt(A) and the underlying regular variation assumption may be recast as P(r(V) ≥ t, θ(V) ∈ A) ≈ t−1Φ(A) ≈ tΦt(A) when t is large. Observe the following error decomposition
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Anomaly Detection in Extreme Regions via Empirical MV-sets on the Sphere
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