User:Mathstat/MVMedian

In statistics, a multivariate median is a location estimate for a multivariate distribution.

Definitions
An affine invariant median 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 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 For a k-variate data set with n observations, the computational complexity is $$O(kn^k log n)$$ for the exact method, and $$O(5^k 1/\varepsilon^2)$$ for the stochastic algorithm where $$\varepsilon$$ is the radius of the L∞ ball.

Affine invariant medians are compared in