Date: Sep 29, 2010 4:12 PM
Subject: Re: Sampling From Finite Population with Replacement
On 29 Eylül, 23:57, Ray Koopman <koop...@sfu.ca> wrote:
> On Sep 29, 12:03 pm, Cagdas Ozgenc <cagdas.ozg...@gmail.com> wrote:
> >>>> The population mean is an unbiased estimate of the generator mean.
> >>>> The sample mean is an unbiased estimate of the population mean,
> >>>> and therefore of the generator mean.
> >>> I think you have a point here. But as you can see that there is a
> >>> problem with consistency.
> >>> Let's say that generator mean is Mu, and population mean is Mu + Eps.
> >>> And I take as you suggest Eps is a random error not a systematic error
> >>> (not a bias).
> >>> Now as you take more and more sample means, you will see that they
> >>> will start to gather around Mu+Eps not Mu. Now do we have a random
> >>> error or a systematic error?
> >> It all depends on whether we're talking about the conditional
> >> distribution of the sample mean, given the population mean; or the
> >> unconditional (or marginal) distribution of the sample mean. As an
> >> estimate of the generator mean, the ssmple mean is conditionally
> >> biased but marginally unbiased.
> > I don't think I am following you. How is all that related to
> > conditioning?
> In the marginal distribution all the error is random, and the sample
> mean is is an unbiased estimate of the generator mean. In the
> conditional distribution there is both random and systematic error;
> the sample mean is a biased estimate of the generator mean, with the
> bias being the unknown but fixed difference between the population
> mean and the generator mean.
Sorry I didn't make myself clear. Basically I am trying to relate your
conclusion to my initial question. What does this in general tell us
about sampling from an infinite population vs sampling from a finite
population with replacement? Can I conclude that they cannot be
treated equally? Why is this issue never mentioned in stat texts?