RE: Question 20

Gyampo, Kofi ( (no email) )
Wed, 4 Nov 1998 10:45:42 -0500

I think the key word is actual sample size. You only approach the asymptotic
value as sample size gets very large. E.g.. Plot y=1/x. Y approaches
asymptote y=0 as x gets very large. For small values of X, y is hardly
equal to zero! Statement is therefore false unless the sample size is large.

> -----Original Message-----
> From: Kongoun, Ross [SMTP:KongounR@aetna.com]
> Sent: Wednesday, November 04, 1998 10:31 AM
> To: 'studygroup4b@lists.casact.org'
> Subject: RE: Question 20
>
> Rao-Cramer lower bound was derived as an approximation to the variance. I
> think the key word in this problem is equal.
>
> > ----------
> > From:
> > Paul.Cohen@uticanational.com[SMTP:Paul.Cohen@uticanational.com]
> > Sent: Wednesday, November 04, 1998 5:21 AM
> > To: studygroup4b@lists.casact.org
> > Subject: Question 20
> >
> >
> > Below is a quote from H&K (pgs 77-78). Please let me know how I am
> > misinterpretting this.
> >
> > "... hence the maximum likelihood estimator is said to be asymptotically
> > efficient because its variance equals this lower bound". In this case
> they
> > are
> > referring to the Rao-Cramer lower bound.
> >
> > Option 2 from #20 on the exam reads "The variance of the estimator is
> > equal to
> > the Rao-Cramer lower bound." According to the above, this statement is
> > true.
> > Since H&K never mention any conditions on this (i.e. small samples), I'd
> > have
> > to say that "C" is the correct answer.
> >