User:Mathstat/MVMedian
In statistics, a multivariate median is a location estimate for a multivariate distribution.
Definitions
[edit]An affine invariant median[1] proposed by Hettmansperger and Randles. The estimator has bounded influence function, positive breakdown value, and high efficiency. Compared with other affine equivariant multivariate medians, it has lower computational complexity.
A median has been defined based on spatial sign statistics, called the Oja[2] median, which is an affine equivariant multivariate location estimate with high efficiency, bounded influence, and zero breakdown. Evaluation of the estimate is computationally intensive. Different computational algorithms are discussed in [3] For a k-variate data set with n observations, the computational complexity is for the exact method, and for the stochastic algorithm where is the radius of the L∞ ball.
Affine invariant medians are compared in [4]
References
[edit]- ^ A practical affine equivariant multivariate median Thomas P. Hettmansperger and Ronald H. Randles, Biometrika (2002) 89 (4): 851-860. doi: 10.1093/biomet/89.4.851.
- ^ Oja, H. (1983). Descriptive statistics for multivariate distributions. Stat. and Prob. Letters, 1, 327–332.
- ^ Computation of the multivariate Oja median, T. Ronkainen, H. Oja, P. Orponen, Metrika (year?) (Volume/Issue?) (pages?)
- ^ Oja, H. (1999). Affine invariant multivariate sign and rank tests and corresponding estimates: a review. Scand. J. Statist., 26, 319–343.
Niinimaa, A.; Oja, H. (2004). "Multivariate Median". Encyclopedia of Statistical Sciences. New York: John Wiley & Sons, Inc. doi:10.1002/0471667196.ess1107.pub2.