regression on order statistics

rs_poetic — Tue, 11 Jun 2013 17:11:04 GMT

In my problem, n bidders place $ bids for unopened lots. They are basing their bids on their judgement of the value of the contents. With bids sorted in order, we have n order statistics, repeated for m lots. I am assuming that a single distribution type generates the bidding, e.g. lognormal or the like. In reality the mean and variance would likely be different for each lot, however to simplify initially I am willing to divide each lot's bids by its high bid. E.g. lot A might have "standardized" order statistics high to low {1, .9, .8, .75, .70. .5,...}. I wish to select a distribution type and its parameters based on these "standardized" sets or order statistics.

PROC UNIVARIATE provides Q-Q plots and methods that readily identify the best distribution and good parameter estimates for each lot. e.g., the Q-Q plot of lot A might be shown to have the best fit to lognormal(.5,1.1).. Of course, if I apply this method to each lot in turn, I get m different results. What I wish is the parameter estimates that are the best fit to data for all lots. Is there a built-in procedure in SAS that does that? or am I on my own to specify a nonlinear regression?

Re: regression on order statistics

PGStats — Wed, 12 Jun 2013 01:34:18 GMT

Dividing by the maximum bid might not be the best strategy, as extreme value statistics have high variance, especially with long-tailed distributions. I would rather try the transformation Yij = log(Bij/Bmj) where Bij is the bid from bidder i on lot j and Bmj is the median bid for lot j. Then I would give it a shot at fitting a single distribution to the whole set of Y's.

Re: regression on order statistics

rs_poetic — Thu, 13 Jun 2013 13:17:20 GMT

Thanks, your approach helps a lot.

topic regression on order statistics in Statistical Procedures

regression on order statistics

Re: regression on order statistics

Re: regression on order statistics