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I'm trying to fit a mathematical/theoretical model to empirical data, but the dataset is impractically big to fit all at once. (Specifically: I'm fitting a power law model using the methods of Clauset, Shalizi, & Newman (2007) - but I think the specific model doesn't matter for this question.)

Is it true that, if I fit multiple 1% random subsets of the data to the best-fit models for those subsets, that the mean of the model parameters will converge on the best-fit models for the full dataset?

This seems to make sense as a consequence of the Central Limit Theorem, but lots of things seem to make sense that aren't true.

Thanks!

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  • $\begingroup$ As a matter of interest - how big? Sample size, range of data. $\endgroup$ – csgillespie Feb 25 '13 at 11:15
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Closing the loop on this for archiving purposes....

A friend explained this to me offline. The answer is YES. Just as the mean of multiple random samples converges on the true population mean (even if the data are highly non-normal), model parameters fit to multiple random subsets will converge on the true model parameters for the population. In fact, bootstrapping in machine learning takes advantage of this phenomenon.

That's what my intuition was, but it's always good to check your intuition.

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