# Method of moments when the first moment is $0$

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?

Thanks!

• 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 $f(\theta) = 0$. – Riley Feb 11 at 3:27
• 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. – NCh Feb 11 at 4:37