论文信息 - Asymptotic theory of the spatial median

Asymptotic theory of the spatial median

In this paper we review, prove and collect the results on the limiting behavior of the regular spatial median and its affine equivariant modification, the transformation retransformation spatial median. Estimation of the limiting covariance matrix of the spatial median is discussed as well. Some algorithms for the computation of the regular spatial median and its different modifications are described. The theory is illustrated with two examples.

K. Nordhausen | H. Oja | J. Möttönen

[1] R. Serfling. Approximation Theorems of Mathematical Statistics , 1980 .

[2] B. M. Brown,et al. Statistical Uses of the Spatial Median , 1983 .

[3] David E. Tyler. A Distribution-Free $M$-Estimator of Multivariate Scatter , 1987 .

[4] Peter J. Rousseeuw,et al. Robust regression and outlier detection , 1987 .

[5] G. Ducharme,et al. Uniqueness of the spatial median , 1987 .

[6] C. Small. A Survey of Multidimensional Medians , 1990 .

[7] C. Radhakrishna Rao,et al. Asymptotic theory of least distances estimate in multivariate linear models , 1990 .

[8] P. Chaudhuri. Multivariate location estimation using extension of R-estimates through U-statistics type approach , 1992 .

[9] P. Chaudhuri,et al. Sign Tests in Multidimension: Inference Based on the Geometry of the Data Cloud , 1993 .

[10] C. Croux,et al. Generalizing univariate signed rank statistics for testing and estimating a multivariate location parameter , 1995 .

[11] Hannu Oja,et al. Multivariate spatial sign and rank methods , 1995 .

[12] Hannu Oja,et al. ON THE EFFICIENCY OF MULTIVARIATE SPATIAL SIGN AND RANK TESTS , 1997 .

[13] M. A. Arcones,et al. ASYMPTOTIC THEORY FOR M-ESTIMATORS OVER A CONVEX KERNEL , 1998, Econometric Theory.

[14] R. Randles,et al. A practical affine equivariant multivariate median , 2002 .

[15] Hannu Oja,et al. On the multivariate spatial median for clustered data , 2007 .