The professor gave us an exercise but for me it's not totally clear. I have a distribution function which depend on a parameter $x$ that I need to estimate. The function describes the distribution of angles $y$ of which I know a sample $y1,..,yn$.
In order to estimate $x$, our professor told us to divide the sample in small groups ( of $3$ or $4$) . For example, I consider $y1,y2, y3 and y4.$ Using these four, I consider the maximum likelihood method to obtain an estimate of $x.$ We call the estimate obtained from the first $4$ samples $x1$ and $z1$ the mean of $y1,y2,y3 and y4$.
By iterating this procedure, I find a vector of estimated parameters $x_i$ and a vector with the means of the small groups $z_i$.
After that I have to do a linear regression (I used $R$), because the final goal was to obtain a formula that relates $x$ to the means $z$, which is because we had divided the sample in small groups.
So in the first step we use the maximum likelihood estimation, then the professor told us that what we do in the final step is an application of the generalized method of moments and we have to explain how we are using this method, but for me it's not so clear, can someone please help me?
He said that this is not exactly the generalized method of moments so I have to explain the relationship and the difference between what I did and the Generalized method of moments. Thanks.