User:Mathstat/MVMedian

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 ${\displaystyle O(kn^{k}logn)}$ for the exact method, and ${\displaystyle O(5^{k}1/\varepsilon ^{2})}$ for the stochastic algorithm where ${\displaystyle \varepsilon }$ is the radius of the L_∞ ball.

Affine invariant medians are compared in ^[4]

Niinimaa, A.; Oja, H. (2004). "Multivariate Median". Encyclopedia of Statistical Sciences. New York: John Wiley & Sons, Inc. doi:10.1002/0471667196.ess1107.pub2.