1
$\begingroup$

I am trying to determine if two regression estimates are different. The first is obtained by ordinary least squares (OLS) and the second is obtained by M-estimation.

As a minimum example, fits for the "Stack Loss Data" (Montgomery et al. 2001 - Introduction to Linear Regression Analysis, pg. 397) are:

OLS: $\hat{y} = -39.9 +0.72x_1 + 1.30x_2 - 0.15x_3$ and M-estimation (Andrews Sine, a = 1.5): $\hat{y} = -37.2 + 0.82x_1 + 0.52x_2 - 0.07x_3$.

Is there a hypothesis test that I could use? From what I've read so far, an ordinary t-test isn't applicable to robust estimates. Please bear with me, I'm a geophysicist who has learned a lot of statistics on the fly.

To clarify, to show that they are different means that they come from different populations, right? From what I understand, M-estimates are asymptotically normal.

Improve this question
$\endgroup$
3
  • $\begingroup$ What is it you're trying to compare exactly? estimates of which quantity? $\endgroup$
    – Glen_b
    Jun 22, 2018 at 3:54
  • $\begingroup$ I'm trying to determine if I can use an approach like this: stats.stackexchange.com/questions/151916/… if one of my regression lines is not the result of OLS. $\endgroup$
    – Jordan Bishop
    Jun 22, 2018 at 19:09
  • $\begingroup$ In very large samples you should still be able to make use of asymptotic normality to derive a chi-squared test from the coefficients and their estimated variance-covariance matrices (assuming you have such estimates) in similar fashion to the answer at the question you point to. $\endgroup$
    – Glen_b
    Jun 23, 2018 at 10:05

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.