[R] "lmomRFA" package: error bounds/confidence intervals

[J. R. M. Hosking]

On 2010-07-21 09:37, Tonja Krueger wrote:
>
>     Dear List
>
>     I’m using the ”lmomRFA” package to fit different distributions to my data
>     sample. To calculate the error bounds I used:
> regsimq(…)
> and
> sitequantbounds(…)
>
> So my questions are:
> Are error bounds and confidence intervals the same thing?

No.  The distinction is explained on page 97 of the book by Hosking and
Wallis cited in the help for 'regquantbounds'.  To paraphrase: error
bounds are constructed similarly to the confidence intervals that arise
from a parametric bootstrap procedure, but are not exact confidence
intervals because (a) there is no pivotal quantity that would allow
exact confidence intervals to be formed and (b) the error bounds
attempt to allow for physically plausible deviations of the data
from the assumed statistical model.

If care is taken in their construction they should display roughly the
same degree of variability as would be seen in the deviations of the
true from the fitted quantiles, and can therefore be used to make, to an
approximation close enough to be useful in practice, the same inferences
that one could have made had exact confidence intervals been available.

> And: Does
>
> regsimq(…  boundprob = c(0.05, 0.95))
>
> calculate the 90 or the 95% confidence interval?

90%

> If error bounds and confidence intervals are not equal: Is there a way to calcu
> late confidence intervals for my fitted distributions (gev, weibull, gumbel…)?

Not that I know of.  The error bounds are intended to be a way of
getting as close as possible to what confidence intervals would be
(or ought to be, given consideration (b) above).


J. R. M. Hosking

>
> Thank you in advance,
> Tonja