Robust Quantile Regression (with robust standard errors)

[Konstantin Fischer]

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.

[Joao Santos Silva]

Dear Konstantin Fischer,

I would start by noting that the so called "robust" regression estimators and quantile regression estimate very different objects. Actually, it is not even clear what "robust" regression estimators estimate; I am very sceptical of such estimators because in a way they choose the data that fits de model rather than fitting a model to the data.

Quantile regression is robust to outliers in the dependent variable and estimates well-defined functions: the conditional quantiles (or an approximation). You can use robust standard errors (check also qreg2) and the method is quite reliable. If the regressors are not significant, either your sample is too small or you need to do more work on the specification of your model.

Best wishes,

Joao