Dear Statalists

I run two robustness regression models (rreg & mmregress) with similar (good) results on my data set (120 observations). The robustness models are chosen due to some outliers/influencing factors. Additionally, I controlled for changes in the results via robust standard errors. The main results are the same; significant levels change to some extend. In the next step, I would like to perform quantile regressions to observe potential non-linear trends and perform an F-Test (Wald-test) on the different quantiles. I know how this works with the Stata command "QREG" and subsequent "test"-function.

However, I run quantile regressions on the prior significant linear robust models and all coef. in the different quantiles remain insignificant.
  • How is it possible that I got no significant coefficients in the quantile regressions? (... even they are in the robustness model)
So, I guess (not sure) I must/should apply a "robust" model as outliers still remain in the dataset? (... and maybe with robust standard errors)
  • Is there an option/command or another (relatively simple) way to perform robust quantile regressions?
Is it an acceptable way to drop the remaining data (keep the quantile I want to observe) and perform the robust regression? If yes, how can I increase (bootstrap?) the small numbers of data in my file to have acceptable performance in the dataset (i.e. small sub-sample)? What would be the simplest way to compare the outcome via Wald-test if I run it manually?

... or did I understood something completely wrong?

If you need further information, please let me know.

THANK YOU for the time / and help. ​​​​​​​