I need to calculate the statistic t (without any softwares or this sort of things) for a linear regression with the robust standard errors already computed. I know that in order to get the t statistic I need to do
t = b1/standard error
Where b1 is the slope coefficient. However, I trying to understand two things (1) how does the robust standard error is used to calculate the statistic t? (2) how does that change the comprehension of the statistic t?
I just couldn figure that out.
The robust standard error is just a way of estimating the standard error. The way you compute and interpret the t-statistic is the same regardless of which standard error you're using.
For (1), if the estimation methodology is BLUE-class, then b1 wouldn't change but robust SE will change. Classic OLS is less robust in the sense that it underestimates SE and hence overestimates t-stats.
For robust SE, there could be an ambiguity in the terminology. a) You estimate b1 with OLS, and then adjust OLS SE somehow to get robust SE (HC or HAC estimators). b) You estimate b1 with robust regression (different from classic OLS), and (non-adjusted) SE can be considered as "robust SE" (robust estimators: M-estimators, ...) Linear regression does not mean OLS: OLS is just one way of doing regressions.
But it usually refers to case a) when you are just saying robust SE.
cf) For biased estimators such as lasso, t-stat interpretations could be different: Null hypothesis in this case is less trivial. (Sometimes coefficients may have different distributions from t-dist. Then just go for p-values. What really matters is p-value, not t-stat.)
