Monday, May 6, 2013

A Visual Proof That OLS is BLU

Back in the day (as they say), we had monochrome monitors on our P.C.'s. Do you remember the ghastly green or weird amber colours? Then, one bright day everything became multi-coloured! This is not just me reminiscing - this is leading up to an innovative proof of the Gauss-Markhov Theorem. Honestly!

In a post yesterday, I mentioned Ken White's sense of humour - that's Ken White, "The SHAZAM Man", as my kids used to affectionately call him. On one of his many visits in the late 1980's, Ken offered to give a talk to a group of students about using the SHAZAM econometrics package. (We had no money for software at the time, but thanks to Ken's outstanding generosity we always had the latest version of his package for everyone to use.)

There were (and probably still are) some hidden tricks in SHAZAM. For instance, if you entered the command "USER KEN", then all sorts of extra things were available to you. For instance, the subsequent commands became case-sensitive. Another command that wasn't widely known was "SET COLOR", which could be rescinded with "SET NOCOLOR". With this option toggled on, the background colour on the monitor changed as certain SHAZAM commands were executed.

I must admit, this got a little hard on the eyes after a while, which might account for my declining vision! However, you have to remember that we didn't have the internet to amuse us, and it really didn't take too much to get us excited - technologically speaking! So, if you issued the command, "READ X", to indicate that a series of data was to be read, the background colour on the monitor turned red.

So, Ken got started on his promo-talk about SHAZAM. The students got right into it. Then he said, "You know, the great thing about SHAZAM is that unlike the competing packages, you can actually use it to prove some important theorems." Now the class got visibly excited!

"For instance", said Ken. "Let's prove the Gauss-Markhov Theorem". He keyed in the command OLS Y  X. As the results began to appear on the screen, the background colour of the monitor turned very bright blue. in response to the use of the OLS command. The colour was so bad that you could hardly see the results.

Dead-pan, Ken said, "And that, my friends, is how you prove that the OLS estimator is BLU!"

© 2013, David E. Giles

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