
Re: Sampling From Finite Population with Replacement
Posted:
Sep 29, 2010 3:09 PM


On Tue, 28 Sep 2010 21:21:42 0700 (PDT), Cagdas Ozgenc <cagdas.ozgenc@gmail.com> wrote:
> >> I agree that the above is ambiguous if you really want to press >> the point. It uses mu and sigma which describe populations >> It does not state whether the population is the class of 2005, >> or something wider that would be more useful for generalization. >> > >That's not the issue. Take any finite population with a data >generating process behind it. Population mean is an unbiased estimate >of data generating process distribution as Ray pointed out. But once >you start getting samples from that population your random error turns >into a systematic error (a bias).
That's clever, but basically wrong. That is not the definition of bias that we have in play previously.
You can get closer and closer to obtaining the value of the population mean; but you never have more precision than what the population mean provides, in regards to estimating the underlying process.
So? That is the error of a single sampling (the "population").
Yes, colloquially speaking, we say that any single drawing of a sample is going to be biased, or it gives a biased estimate. But the relevant meaning when we speak of "an unbiased statistic" is limited to the venue of the procedure that is being repeated.
Subsamples give an unbiased estimate of the sample. The sample gives an unbiased estimate of the generating process  and the mean of the whole sample has smaller error than any of its subsamples will have. Technically, we want to say that subsamples *do* give an unbiased estimate of the generating process, (inevitably) with larger error than the whole sample.
The prospect of misstatement arises from imagining that using the subsamples can escape the original error of the sample. Even though we may casually call it "biased" when we describe its effect, that is applying the adjective on a different level of intercourse.
 Rich Ulrich

