🚀 go-pugleaf

In article <muzic.713536981@ds2.uh.cwru.edu> muzic@ds2.uh.cwru.edu (Ray Muzic) writes:
>I have 2 references that give different answers.  I believe one of the
>answers is restricted to the case of a model that is linear in the
>parameters.  However, I seem to recall that for a nonlinear model, an
>approximation that the model is linear about the optimum point is often
>employed.  Does this mean the covariance of the parameter estimates may be
>estimated assuming the model is linear about the operating point?
>

  The suggested linearization produces an approximation to the parameter
  covariance matrix that is less than first order accurate.  A true
  first order approximation contains second order derivatives of the
  model function.  For a derivation and discussion of the corresponding
  formula see

   A. Celmins, Least-Squares Optimization with Implicit Model Functions, in
   "Mathematical Programming with Data Perturbations II", Anthony V. Fiacco,
   Ed., Marcel Dekker, 1983, pp. 131-152.

  The covariance computation is discussed on pp. 136-138.
 
  Aivars Celmins