Interesting. Thanks Erin, Josef and Keith. There is a nice article on this at http://www.stata.com/support/faqs/stat/supweight.html. In my case, the model I've in mind is to assume that the expected value (mean) is the same for each sample, and that the weights are/should be normalised, whence a consistent estimator for sem is straightforward (if second moments can be assumed to be well behaved?). I suspect that this (survey-like) case is also one of the two most standard/most common expression that people want when they ask for an s.e. of the mean for a weighted dataset. The other would be when the weights are not to be normalised, but represent standard errors on the individual measurements.
Surely what one wants, in the end, is a single function (or whatever) called mean or sem which calculates different values for different specified choices of model (assumptions)? And where possible that it has a default model in mind for when none is specified? thanks, Chris On Thu, Sep 9, 2010 at 9:13 PM, Keith Goodman <[email protected]> wrote: > >>>> ma.std() > >> 3.2548815339711115 > > > > or maybe `w` reflects an underlying sampling scheme and you should > > sample in the bootstrap according to w ? > > Yes.... > > > if weighted average is a sum of linear functions of (normal) > > distributed random variables, it still depends on whether the > > individual observations have the same or different variances, e.g. > > http://en.wikipedia.org/wiki/Weighted_mean#Statistical_properties > > ...lots of possibilities. As you have shown the problem is not yet > well defined. Not much specification needed for the weighted mean, > lots needed for the standard error of the weighted mean. > > > What I can't figure out is whether if you assume simga_i = sigma for > > all observation i, do we use the weighted or the unweighted variance > > to get an estimate of sigma. And I'm not able to replicate with simple > > calculations what statsmodels.WLS gives me. > > My guess: if all you want is sigma of the individual i and you know > sigma is the same for all i, then I suppose you don't care about the > weight. > > > > > ??? > > > > Josef _______________________________________________ NumPy-Discussion mailing list [email protected] http://mail.scipy.org/mailman/listinfo/numpy-discussion
