I've been dealing with the problem of how to construct confidence intervals on penalized spline estimators in the presence of cluster-wise auto-correlation and heteroskedasticity. My previous thread on this is here: Penalized spline confidence intervals based on cluster-sandwich VCV

One of the commenters suggested using a wild bootstrap. This is a bit tricky in the presence of clustered data, but this paper by Cameron et al. at UC Davis proposes what seems to be a relatively simple approach that accommodates the clustered context: http://ideas.repec.org/a/tpr/restat/v90y2008i3p414-427.html

Basically, the residual vector for each cluster has an equal chance of being left alone, or being multiplied by -1. Thats it. No resampling. Over many iterations, you get many different combinations of cluster-wise residual vectors, but your combinations are restricted to the set of residual vectors that you already have, potentially multiplied by -1. (I'm aware that there are alternative things that you might multiply your residual vector by, summarized on wikipedia: http://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29#Wild_bootstrap)

Basically this all seems too simple. Am I missing some complicating wrinkle?

Given that I'm programming my own estimators in R, I need to program my own bootstraps as well. I want to make sure I get the procedure right before I go and code.

Thanks in advance.

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    $\begingroup$ At first sight, it does seem absurd that something that simple would work, but it does. $\endgroup$ – tchakravarty Dec 6 '12 at 3:54
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    $\begingroup$ you know, so many things in stats would benefit from simple english explanations. so often, I find myself reading some paper explaining some method or estimator. it sounds really complicated and hard until I finally get it. and then I realize that it is the simplest thing in the world, but that the simplicity is obscured by too much complication and poor writing. all the math is of course required, but a lot of papers would benefit from a "colloquial" section, in which things are explained at a level where the average educated person could get the gist at a glance. $\endgroup$ – generic_user Dec 6 '12 at 6:18

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