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Despite years of stat courses I'm afraid I may still not completely understand bootstrapping.

My question here relates to nonparametric boostrapping of regression models. As i understand it you draw N bootstrap resamples of your original data to approximate the true n^n possible bootstrap samples, which in turn approximate the true underlying distribution.

However, if you were to draw all n^n, that would include rank deficient samples of the form (X1, X1, X1,... X1) for which there isn't a unique regression estimate. Even if you only do N resamples, there is still some non-zero probability mass on the rank-deficient resamples.

So how can the nonparametric bootstrap actually give you any meaningful result?

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