[R] Complex sample variances

Thomas Lumley tlumley at u.washington.edu
Tue Apr 13 22:11:17 CEST 2004

On Tue, 13 Apr 2004, Fred Rohde wrote:

> Looked through the publication, "Statistical Methods and Mathematical
> Algorithms Used in Sudaan" (Shah, et al, 1993) but the only reference to
> variances on quantiles is a 1991 presentation by David Binder.  Googled
> the title and got this link.
> http://www.amstat.org/sections/srms/Proceedings/papers/1991_005.pdf

Ok.  I see.

I wouldn't have called this a Taylor series method, and I notice that
Binder agrees with me.  They are doing interval estimation by inverting a
score test, which is an interval estimation method I want to add more
generally in R.  It works much better than Wald tests for a number of
quasilikelihood/estimating function estimators in ordinary model-based
analysis, too.

Taylor series methods have trouble with quantiles because the estimating
function isn't differentiable.  Asymptotic normality still applies, but
the asymptotic standard error depends on the density of the variable at
the quantile, and the asymptotic approximation is not as good as usual.
Even the bootstrap needs larger sample sizes for quantiles than for many


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