# (Quantile regression) Which standard error for heteroscedasticity & serial correlation

I have heteroscedastic and autocorrelated residuals in my multivariate quantile regression model.

What's the quantile regression standard error estimator that's robust to this? Something hopefully like HAC Newey West but for quantile regression, or perhaps a bootstrap.

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The bootstrap is almost always good for getting standard errors in complex modeling situations. I am not as familiar with the bootstrap literature on this topic. I do know that naive application of the bootstrap does not work on the extreme order statistics. I am not sure what difficulties this might impose on this particular problem. –  Michael Chernick Oct 3 '12 at 11:19
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## 1 Answer

You're definitely going to want to bootstrap. Have you looked at the R package "quantreg"?

http://cran.r-project.org/web/packages/quantreg/quantreg.pdf

There's a function, boot.rq, for bootstrapping a standard quantile regression. For B bootstrap replications, the function gives you B estimates for each parameter. The standard error for each parameter estimate is just the standard deviation of the B estimates.

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Yeah I use quantreg for all my QRs. Which bootstrap am I using (I should have specified my question better, I knew it would come down to a bootstrap)? –  user14281 Oct 3 '12 at 13:04
Not quite sure what you mean by "which" bootstrap - it should just be the boot.rq function unless your data are censored. –  wcampbell Oct 3 '12 at 13:07
There's 5 types. From the package "bsmethod The method to be employed. There are (as yet) five options: method = "xy" uses the xy-pair method, and method = "pwy" uses the method of Parzen, Wei and Ying (1994) method = "mcmb" uses the Markov chain marginal bootstrap of He and Hu (2002) and Kocherginsky, He and Mu (2003). The fourth method = "wxy" uses the generalized bootstrap of Bose and Chatterjee (2003) with unit exponential weights, see also Chamberlain and Imbens (2003). The fifth method "wild" uses the wild bootstrap method proposed by Feng, He and Hu (2011). " –  user14281 Oct 10 '12 at 11:27
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