In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%.[1] Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine transformations that combine both variables.[1] It can be calculated in time by brute force, in time using more sophisticated techniques,[2] or in randomized expected time.[3] It may also be calculated using an on-line algorithm with update time.[4]
The repeated median method estimates the slope of the regression line for a set of points as
where is defined as .[5]
The estimated Y-axis intercept is defined as
where is defined as .[5]