Abstract #300320

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JSM 2002 Abstract #300320
Activity Number: 336
Type: Invited
Date/Time: Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
Sponsor: Section on Physical & Engineering Sciences*
Abstract - #300320
Title: Oscar Kempthorne and the Distribution of Quadratic Forms
Author(s): David Harville*+
Affiliation(s): IBM T. J. Watson Research Center
Address: P.O. Box 218, Yorktown Heights, New York, 10598, U.S.A.
Keywords: Statistical independence ; Multivariate normal distribution ; Linear statistical models ; Distribution of quadratic forms ; Noncentral chi-square distribution ; Laha's lemma
Abstract:

What constitutes acceptable and appropriate proofs of the standard results on the distribution of quadratic forms (in normally distributed variates) has long been a point of contention. Most anyone who has taught a graduate-level course on linear statistical models has wrestled with this issue. Oscar Kempthorne was no exception.

I will discuss various of the proofs that have been proposed, and offer some opinions. My thinking on this topic was influenced to a considerable extent by discussions with Kempthorne, though those discussions did not always lead to agreement. Following one such discussion, Kempthorne came up with an idea for proving a key result (known as Laha's lemma) on polynomials. His proof, which I subsequently "fleshed out" and eventually included in a jointly authored publication, is somewhat tedious but (in regard to mathematical level) highly accessible.

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Revised March 2002