method of moments with variance=$\sigma^2$ I am trying to estimate the value of a parameter by equating variance from a distribution to the sample variance... i.e. using method of moments estimation. Would it better to use the variance formula with $1/(n-1)$ in the denominator or $1/n$? Why is one better than the other?
thanks

I'll give an example: say I have been told Random variables from the 'geometric distribution' have a $\sum_{1}^n(X_i - \bar{X})^2$= 10. Then in order to estimate the parameter 'p' where $\frac{1-p}{p^2}$ is the variance of the geometric distribution.
do I in this circumstance use: $\frac{10}{n-1}=\frac{1-p}{p^2}$ and then given 'n' solve quadratic for p. or should I be using $\frac{10}{n}$ instead on the LHS.
 A: Regarding the method of moments and you question you can find the answer here in Wikipedia.
When given a family of distributions where the distribution is determined by the value of one or more unknown parameters you can take the non central moments and given that they are a function of the unknown parameters solve k equations in k unknowns where the k equations equate the first k non central moments to the function of the parameters that they are equal to.  Use the sample estimate for the moments and then solve for the parameters.  If you have k parameters you have to have a case where the first k moments exist to solve.  The sample moments are for a sample X$_1$, X$_2$,...,X$_n$ given by
jth moment: ∑X$_i$$^j$ /n  where i runs from 1 to n and j can be 1, 2, ...,k.
So you don't need to compute a sample variance and you don't need to consider the issue of choosing between n and n-1.  The method of moments was devised by Karl Pearson prior to Fisher's development of maximum likelihood.  When the mle exists (regular cases) it has efficiency advantages over the method of moments.  The Wikipedia link explains the pros and cons of using method of moments.  The method of moments cannot be applied if the first moment doesn't exist even when k=1.  But the mle may still exist and be efficient. 
