[R-sig-ME] "confidence intervals" and "nominal levels"

[Ben Bolker]

  Context?

  I'm assume that some algorithm or piece of software is returning an
interval that claims to be a frequentist confidence interval (CI), which
by definition means that x% of the time (people usually quote 95% CIs,
but other values are possible) in a long run of repeated
experiments/observations the CIs would contain the true value of the
parameter.

  So "confidence intervals below the nominal levels" probably means that
the CIs from the algorithm/software are *undercovering* -- they contain
the true value *less* than the nominal percentage (x%) of the time, or
equivalently they are narrower (more optimistic) than they should be.

 Typically in order to know something about the coverage (i.e. the
fraction of repeated trials that *actually* continue the true value) one
has to do a simulation study (it's not impossible to derive such things
analytically, but it's usually impractical except in very simple cases).

  cheers
    Ben Bolker

On 2019-03-27 12:21 p.m., Mario Garrido wrote:
> Hi,
> a brief and probably too simple question.
> What is mean that the "confidence intervals" is below the "nominal levels"?
> Thanks
>