Given $X_1,X_2,\ldots,X_n \sim $ Cauchy Distribution ${C(\theta,1)}$, what is a method of moments estimator of $\theta$?
$\theta^* = \text{mean}$ is the method of moments estimator for Cauchy Distribution. For Cauchy Distribution Moment Generating function is not defined so can we calculate the method of moments estimator for it?