Im currently reading about unbiased estimators which I think is when you use the distribution of samples to estimate the mean and standard deviation of a population. Please correct me if I'm wrong.
I've understood the proof that shows that E(X bar) = u (population mean)
and Var(X bar) = sigma squared over n
Now I'm coming across another formula for Variance= (?X^2-nXbar^2)/n-1
Is this equivalent to sigma squared over n? Is it called the sample variance, like ?X/n is called sample mean?
Also, can someone please explain this concept of bias to me? Whats the difference between a biased and unbiased estimator? If an estimate of E(X bar) wasn't equal, to "u" this wouldn't necessarily mean it was biased would it?
Sorry, im just really confused with these concepts and am trying to self teach this module :/ If you know of any good websites to get help with s3 please let me know.
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S3 Estimation watch
- Thread Starter
- 20-03-2011 11:45
- 20-03-2011 12:34
If the expected value of an estimator is equal to a population parameter then we say that the estimator is unbiased.
It can be proved that if S^2= (n/n-1)*(sum X^2/n - (Xbar^2)) or equivalently (?X^2-nXbar^2)/n-1 as you write,
then E(S^2)= sigma, the population variance. So S^2 is an unbiased estimator for the population variance sigma.