I have a quick question regarding the method of moments estimator.

Generally, when you have $k$ parameters you want to estimate, it suffices to find $k$ equations using $k$ moments.

If you are estimating one parameter, and you find that the first moment is equal to $0$, what do you do? Do you find the second moment and use that as the estimate?


  • 1
    $\begingroup$ In the case $k = 1$ and you have a single parameter $\theta$, if the mean is given by $f(\theta)$ and your first moment is zero then this is just the same as solving $f(\theta) = 0$. $\endgroup$ – Riley Feb 11 at 3:27
  • 2
    $\begingroup$ Yes, you should take second moment to construct estimator. Say, in the case of uniform distribution on $[-\theta,\theta]$ MOM for $\theta$ cannot be constructed from the first moment. $\endgroup$ – NCh Feb 11 at 4:37

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