Robust Residual standard error (in R)

Question

I have a question regarding to the concept of robust standard errors. What I found about that topic is, that one can estimate the robust standard error for regression coefficients to eliminate problems with heteroscedasticity (when one wants to interpret a model). I want to know if there is a way not only to determine robust standard errors of coefficients but also of the standard error of the overall regression (residual standard error). When its possible, how can I calculate such a value in general?

Because I'm using R its also interesting for me if there is a R-function for this problem (I only know the sandwich-package for the normal robust SE of the coefficients).

Thanks.

Is it still the policy of Cross Validated to refer problems relating to statistical packages to StackOverflow? — Cesare Camestre, Aug 26 '13 at 15:29
It depends, @CesareCamestre. If the question is about how to *use* R, such that an explanation of the ideas w/o reference to R, or demonstrated w/ different software, eg Stata, would not answer the question, then it belongs on SO. But if the issue is w/ understanding the ideas, then it can stay here, even if they as about R as well. (Which of the above applies to this Q is not clear to me yet.) — gung - Reinstate Monica, Aug 26 '13 at 15:33
Welcome to the site, @Meiner. It is not clear to me if you are wondering about the nature of sandwich estimates, or if you are *only* wondering about another way to implement them in R. If the latter, this question would be off-topic for CV (see above), but on-topic on [Stack Overflow](http://stackoverflow.com/). If your question is about the underlying ideas, please edit to clarify; if it's about implementation in R, flag your Q & we'll migrate it for you (*please don't cross-post, though*). — gung - Reinstate Monica, Aug 26 '13 at 15:37
Do you mean forming confidence bands for predicted values or creating something like a global test for all regression parameters against a null intercept-only model? — AdamO, Feb 13 '18 at 21:26

score 2 · Answer 1 · answered Oct 29 '18 at 16:25

If you are interested in the conditional mean $\mathop{\mathbb{E}} \bigl[ y_j|X_j \bigr] = X_j' \beta$, where $X_j$ may be in or out of sample, then of course you can get the standard error for that as the square root of $$ X_j' \, \hat v[\hat \beta] \, X_j $$ where $\hat v[\hat \beta]$ is the heteroskedasticity-corrected/sandwich variance estimator. But that conditional mean is rarely of huge interest; I believe you are interested in characterizing what the whole distribution of $y_j = X_j + \varepsilon_j$ may have looked like. Without knowing more about the distribution of $\varepsilon_j$ you, of course, won't be able to say much about what the variance of $y_j$ will be.

Robust Residual standard error (in R)

1 Answers1