
Re: Sampling From Finite Population with Replacement
Posted:
Sep 29, 2010 4:12 PM


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?

