What is the formula for the Unbiased estimator (for mean and
variance)? And how and why does it work?
Hal
unbiased mean = sample mean
unbiased variance = n/(n-1) x sample variance
be back for an explanation
dimitri
Y is an unbiased estimator for a
quantity c if we have
E(Y)=c
that is, the expected value of Y is c. So you can take any
quantity whose expected value is c, and this is an unbiased
estimator. The ones Dimitri quotes are the standard ones - it's
easy to show they have the required property. In specific
situations, there are other unbiased estimators and in this case
you have to use other methods to decide which is the "best"
one.
For example, sample mean is
sum(Xi )/n
and the expectation of a sum is the sum of the expectations so
expected value of sample mean is sum(mean)/n which is of course
simply the mean. The variance is slightly more tricky, but
follows a similar pattern.
-Dave
By S2 do you mean the
variance? We normally use sigma instead of S. The answer is yes,
because n/(n-1) tends to 1 as n tends to infinity.
But do you know what "consistent" means in this context?
-Dave