Thank you for the answer, I wasn't aware I'm talking with an accomplished professor to say the least.
I think I can modify my model to a Gaussian mixture model instead of normal distribution and perhaps use LRT to measure how many parameters I need in order to stay in a confidence interval. I have to think about it...
Do you mind giving a reference for your paper on atomic mass? I'm a physicist and I'm curious to see how you managed to do it, probably more than a decade before the first IBM personal computer.
Not quite as far back as I said .. the paper where I first used an
F-test for significance of added terms was in 1967:
P.A. Seeger in Barber, R.C., ed.:
Proc. 3rd Intern. Conf. on Atomic Masses, University of Manitoba Press, Winnipeg, 1967, p. 85.
There is a pretty good version in the Third Edition of the American Institute of Physics Handbook (1972), p.
8.92-
8.142
The most-often referenced is
P. A. Seeger and W. M. Howard, “Semiempirical Atomic Mass Formula,”
Nucl. Phys. A238 (1975) 491-532.
BTW, we used least-squares for fitting, as the procedure was well developed. Computers used were IBM7094 and CDC6600. The key routine was a double-precision matrix inversion subroutine from Brookhaven, for up to a 20×20 matrix. Doing the actual matrix inversion gives the Variance-Covariance matrix as a result.
Nowadays you might consider Maximum Liklihood, based on "information" or entropy, rather than least squares. This is a logarithmic approach, as is the Liklihood Ratio Test.