#StackBounty: #distributions #fitting #method-of-moments Method of moments for symmetric mean zero distributions

Bounty: 100

When using the method of moments to fit a symmetric mean zero distribution, does it make more sense to fit higher order moments or lower order absolute moments? I could not find any resources which discuss/compare the merits of these two approaches.

My intuition is that with fewer observations it would be preferable to fit the absolute lower order moments which will be a more stable estimation (just a guess). In practice (in industry not academia) I have seen both methods used (usually the method that is easier to solve analytically…).

Get this bounty!!!

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