```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 yourconclusion to my initial question. What does this in general tell usabout sampling from an infinite population vs sampling from a finitepopulation with replacement? Can I conclude that they cannot betreated equally? Why is this issue never mentioned in stat texts?
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