Order statistics

February 20, 2019 — March 17, 2020

ordinal
probability
regression
statistics

For a sample of independent observations X1,X2,,Xn with common distribution F the ordered sample values

X(1)X(2)X(n) are called the order statistics.

Todo: connection to maximum processes, learning ranking, simplex

Hung Chen’s notes are good.

Gwern did some fun engineering of order statistics, which edges around some general properties of joint maximal statistics of elliptical copulas.

My one-weird-trick in this domain is for sums of top-kth of N i.i.d. exponential random variables, which turn out to have a simple representation in terms of k random exponentials (). The magic is that quantile transforms make this into a very general way of doing cheap order statistics for i.i.d. variables.

1 References

Nagaraja. 2006. Order Statistics from Independent Exponential Random Variables and the Sum of the Top Order Statistics.” In Advances in Distribution Theory, Order Statistics, and Inference.