Edgeworth and the Newsvendor

Several months ago I received a new paper by Mukherjee, Brown and Rusmevichientong on
empirical Bayes methods for the "newsvendor problem."  It is a matter of considerable personal
embarrassment that I hadn't ever heard about the newsvendor problem.  In its simplest form we
have a newspaper vendor (remember them?) who must decide how many papers of various sorts
he should stock.  He sacrifices profits if he stocks too many or too few, the loss is linear in both
directions, but asymmetric.  He knows the distribution, F, of the (random) demand for each
paper, and of course his solution is to stock the a/(a+b) quantile of F, where a is the marginal
cost of stocking too few papers, and b is the marginal cost of stock too many.  I learned this
bit of basic decision theory wisdom from Tom Ferguson's wonderful textbook in a course from
Bruce Hill eons ago, and I was aware that it appears in Raiffa and Schlaifer's text as well, but
I was surprised to learn that there was an extensive operations research literature going back
at least to the seminal paper of Arrow, Harris and Marschak in 1951.  Why I was surprised,
since this is a rather fundamental problem in inventory policy, is another question, but I won't
delve into that. *  Instead, I decided to look into the earlier history of this idea and began to see
quite a lot of references to Edgeworth's (1888) paper "The mathematical theory of banking."
More embarrassment ensued when I realized that I'd never read this paper.  Reading it revealed
a very clear formulation of the newsvendor problem applied to banking, unfortunately Edgeworth's
solution seemed a little murky.  I've tried to untangle all this in a couple of pages below, but as
you will see, it resists a fully satisfactory untangling.

Edgeworth.pdf

* I would like to stipulate that the simple static model underlying the newsvendor problem
is only a small part of the accomplishment of the AHM paper that introduced dynamic sS
rules as well.

The Pianists' Birthday Problem

We are used to the idea that common birthdays are not that unusual.  I recently attended a
chamber music concert involving the young German pianist Markus Groh.  A quick look at
his website revealed a rather extreme version of birthday matching:  Groh was born January 5th,
the same day as Alfred Brendel, Maurizo Pollini, and Arturo Benedetti Michelangeli!

Requirements for Academic Work

Inquiring minds often wanted know:  What sort of qualifications were necessary for academic
positions?  Finally we have an answer from the University of Arkansas.  In addition to passing
background checks for prior criminal records one must be capable of:

Sedentary Work - Exerting 10 pounds: Occasionally, Light Work - Exerting up to 20 pounds: Occasionally, Kneeling: Occasionally, Climbing (Stairs, Ladders, etc.): Occasionally, Lifting 5 -10 lbs: Occasionally, Lifting 10-25 lbs: Occasionally, Carrying 5-10 lbs: Occasionally, Pushing/pulling 10-25 lbs: Occasionally, Sitting for long periods of time: Occasionally, Standing for long periods of time: Occasionally, Speaking; Essential, Hearing: Essential, Vision: Ability to distinguish similar colors, depth perception, close vision: Essential, Walking - Short Distances: Frequently, Walking - Moderate Distances; Occasionally.

Ab Uno Disce Omnes

Virgil's dictum:  "From one example, all is revealed,"  would seem to be the very antithesis of
statistical thinking, so it seems surprising to discover that a single observation is enough to
construct a confidence interval for the mean in the standard Gaussian model with unknown
mean and variance.  The construction is described below and comes from class notes of Charles Stein,related to me by Steve Portnoy.  Any further information about the origins of this problem
or its solution would be most welcome.

Details in html
Details in pdf

Pricing the Internet

More or less by accident I ran across http://www.dtc.umn.edu/~odlyzko/doc/smart.pricing.pdf
an analysis of prospects for internet pricing by Andrew Odlyzko, an old Bell Labs hand now
at the U. of Minnesota.  He makes the case against congestion pricing, arguing that consumers
and perhaps business as well prefer simple flat rates, i.e. usage independent pricing and that
technology is capable of expanding to meet this preference.  Having argued the other side
of this case in http://comjnl.oxfordjournals.org/content/27/1/8.full.pdf  long ago, I was a bit
surprised,  and am still not entirely persuaded.  Maybe this only reflects that I haven't fully
accepted recent developments in behavioral economics?

Amsterdam Econometrics Games 2015

This year for the first time we sent a UIUC team
to the Econometric Games in Amsterdam.  This is a 3 day competition among
30 Universities; there is a preliminary round to select 10 finalists and then a
second round to determine the three prize winners.  The topic this year was
Longevity and Longevity Risk.  Details of this year's competition are available
here   http://www.econ.uiuc.edu/~roger/EGames/Case1.pdf   and
here  http://www.econ.uiuc.edu/~roger/EGames/Case2.pdf

Our team:   Nicolas Bottan, Cesare Buiatti, Julia Gonzalez and Jiaying Gu
placed second in this competition outperforming perennial favorites like
Copenhagen, Aarhus, Amsterdam, Carlos III as well as Oxford, Cambridge
and Harvard.  Our team deserves a ticker tape parade when they return
this weekend, unfortunately ticker tape is scarce these days.  So we will have
a celebration of their remarkable achievement on April 17th as part of the
Fourth Annual Boneyard Conference of Econometrics.  Details here:
http://www.econ.uiuc.edu/~roger/seminar/Boneyard15.pdf

So the time has come put your brackets on the table, here is a random realization of a bracket from
the QBracketology model complete with scores, and survival curves for the various teams based on
1000 realizations of the Tournament.  As you can see, not surprisingly, Kentucky is an overwhelming
favorite, with a probability of 0.407 of winning.  Only time will tell whether the estimated probabilities of the model are competitive in the Kaggle competition.