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In stata, robust regression (rreg) uses weights proportional to the size of the residuals. Is this conceptually the same as weighted OLS (weight by 1/variance)? And both can be applied, for example, in scenarios with heteroskedasticity?

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They are not the same, because in weighted OLS, weights are given apriori, they are not a function of size of residuals, as in some types of robust regression. However, there is a connecteion, as robust regression sometimes can be calculated via IRLS, iteratively reweighted least squares. For the last, see can you give a simple intuitive explanation of IRLS method to find the MLE of a GLM?

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  • $\begingroup$ +1 which would you choose for linear regression with heteroskedasticity? $\endgroup$ – bobmcpop Oct 14 '17 at 9:33

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