Date: Sep 29, 2010 4:12 PM
Author: cagdas.ozgenc@gmail.com
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?