I would like to check if two subpopulations of my data have the same parameters in a model. Model 1 is based on subpopulation 1 and Model 2 is based on subpopulation 2.
Model 1: $y=x^\alpha + \gamma +\varepsilon$
Model 2: $y=x^\beta+ \theta +\varepsilon$
The parameters of the two models are estimated with Nonlinear Least Squares.
The hypothesis I want to test is therfore:
H0: $\gamma $ = $\theta$ and $\alpha = \beta$
Normally I would use an Chow-test/F-test to test this hypothesis. However the residuals ($\varepsilon$) of the two models are heavy tailed. Since the F-test is sensitive to non-normality and will probably result in small p-values I would like to use another test. What test would be suitable?