[Gretl-users] Re: Idempotency of residual maker matrix
On Mon, 11 Jan 2021, Alecos Papadopoulos wrote:
gretl 2020e Windows 64
I created a "residual maker" matrix M = I - X*inv(X'X)*X', which is
symmetric, non-invertible and idempotent. Below I have copied its properties
as printed out by gretl. It clearly states that the matrix is "Not
idempotent".
But It is, in theory and it is in practice: I performed the operation M*M -
M, and I got a matrix with zeros or numbers raised to the 10^{-16} or even
smaller.
*What does it take for gretl to characterize a matrix as idempotent?*
You're right, we were not taking finite precision into account. Here's a
minimal script for creating a falsely not idempotent matrix:
<hansl>
set seed 123
n = 10
k = 3
X = mnormal(n, k)
M = I(n) - qform(X, invpd(X'X))
</hansl>
I just committed to git a fix which seems to work.
@Allin: my fix changes the signature of a libgretl function; I'm fairly
confident I ran all the checks so it doesn't break anything, but please
review.
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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