Thanks Jack!

Alecos Papadopoulos PhD
Athens University of Economics and Business
web: alecospapadopoulos.wordpress.com/
scholar:https://g.co/kgs/BqH2YU

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.

-------------------------------------------------------
  Riccardo (Jack) Lucchetti
  Dipartimento di Scienze Economiche e Sociali (DiSES)

  Università Politecnica delle Marche
  (formerly known as Università di Ancona)

  r.lucchetti@univpm.it
  http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------

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