This letter deals with the case where parameter estimation is required, but only observations of extreme values (i.e., the minimum observed value and/or the maximum observed value per interval) are available. We describe the theoretical grounds of the three leading methodologies of estimation from extremes, discuss the relations between them, and analyze the tradeoffs of the different methodologies with respect to the performance (accuracy), complexity, and robustness of the estimates. We then demonstrate our evaluations via a specially designed simulation, which validates our results.
- Extreme value theory
- maximum likelihood estimation
- parameter estimation