I have a set of 990 samples with size=3 (n=3). All come from a different finite population (size between 10 and 20). Each population has its own mean, which is known, but it is reasonable to assume that they have equal variance. Therefore I substracted the known means from the sampled values. That gives 2970 values ($990*n$), lets name them $Y_i$ with $i=1,\dots,2970$. My reasoning was that the sample variance of these values would be an unbiased estimate of the variance in each finite population.

  1. Is that correct so far?

Then I would want to estimate the variance of the sample mean for different sample sizes. I thought of bootstrapping by resampling the desired sample size from $Y_i$ with replacement giving each time a value of $\bar{Y}^*_j$ for bootstrap sample $j$. I would then estimate $var(\bar{Y})$ as is traditionally done in bootstrapping and multiply with a Finite Population Correction (FPC) so the estimator becomes:

$$ Var(\bar{Y}) * \frac{N-n}{N-1} $$

  1. Is it correct to use FPC in combination with a bootstrap variance estimate, or do you have other suggestions?

Thanks for your help!



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.