摘要: LetX be ak-dimensional random vector with mean vectorμ and non-singular covariance matrix Σ. We show that among all pairs (a, Δ),a ∈ IR k , Δ k×k positive definite symmetric andE(X−a)′ Δ−1(X−a)=k, (μ, Σ) is the unique pair which minimizes det Δ. This motivates certain robust estimators of location scale.
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sci-hub.se 参考文章(3)
P. L. Davies, Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices Annals of Statistics. ,vol. 15, pp. 1269- 1292 ,(1987) , 10.1214/AOS/1176350505
Elvezio M. Ronchetti, Peter J. Rousseeuw, Werner A. Stahel, Frank R. Hampel, Robust statistics: the approach based on influence functions ,(1986)
Peter Rousseeuw, Multivariate estimation with high breakdown point Reidel. ,(1985)