Thursday, November 11, 2004

A victory for robust statistics ?

In all the brouhaha over election predictions, it is worth observing that robust statistics scored a clear victory.

According to Wes Colley and J. Richard Gott, merely taking the median of all polls in the last month was good enough to predict the election outcome with almost 100% accuracy (they got Hawaii, with only 2 polls, wrong).

And what is a robust statistic ? One way of defining it is that it is a statistic on a set of numbers that requires at least a constant fraction of the input to go to infinity before the statistic itself goes to infinity (for the median, this number is 50%; however, only one number needs to go to infinity to pull the mean along with it). A robust statistic is often useful as a non-parametric measure of a data set that is sensitive to outliers; one of the best examples in two dimensions is Tukey's halfspace depth.

Aren't elections educational ?