Internal analysis and optimization applied to parameter estimation under uncertainty

We present a methodology through exemplification to perform parameter estimation subject to possible factors of uncertainty. The underlying optimization problem is posed in the framework of the theory of interval-valued optimization. The implementation of numerical procedures required to achieve efficient solutions implied the use of the $\ell_1$ norm instead of usual $\ell_2$ regression. Finally, an implementation using real data was performed, demonstrating the ability of interval analysis to encapsulate uncertainty while facing non-trivial parameter estimation problems.