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*{y1,y2,...,yk}*realisations of a random variable

*Y*, and let

*S(k)*denote the variance of the sample as a function of its size; that is

*S(k)=1/k( ∑*y¯

^{k}_{i=1}(yi−*)*

^{2})for y¯

*=1/k( ∑*

^{k}_{i=1}yi)I do not know the distribution of Y, but I do know that S(k) tends to zero as

*k*tends to infinity.

Suppose that I can increase the sample size gradually, so that I can calculate a sequence of variances

*{S(1),S(2),...,S(k)}*for any strictly positive integer

*k*.

I would like to determine the sample size that guarantees a minimum (arbitrary) 'degree of convergence'; in other words, I would like to determine the minimum value of

*k*for which we expect that

*S(k+1)=S(k)±ϵ*, for some small ϵ.

Ideas? I'm not interested in the analytical answer to this question, but rather something that I can implement numerically.

NOTE: This question has also been asked here