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Re: Sampling From Finite Population with Replacement
Posted:
Sep 29, 2010 3:57 PM
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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.
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