Interval analysis and optimization applied to parameter estimation under uncertainty

Abstract

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 ℓ1 norm instead of usual ℓ2 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.