MoM vs MLE Comparison¶
Overview¶
We compare the Method of Moments and Maximum Likelihood Estimation across several criteria.
Comparison¶
| Criterion | MoM | MLE |
|---|---|---|
| Computation | Often closed-form | May require optimization |
| Efficiency | Generally less efficient | Asymptotically efficient |
| Consistency | Yes (under regularity) | Yes (under regularity) |
| Invariance | No | Yes |
| Robustness | Moderate | Sensitive to model misspecification |
When to Use Each¶
- MoM: Quick estimates, starting values for MLE optimization, when likelihood is intractable
- MLE: When efficiency matters, when model is correctly specified, when asymptotic theory is needed