On Nonparametric Isotonic Regression and Model Calibration

Specialeforsvar: Rasmus Vester Munkner

Titel: On Nonparametric Isotonic Regression and Model Calibration

Abstract: We treat the nonparametric, isotonic regression problem within the class of scoring functions that are consistent for an identifiable functional and absolutely continuous in their first argument. We show that for this class of regression problems there exist a simultaneously optimal solution and provide a provably correct algorithm that computes the solution when the set of covariates is totally ordered. We proceed to show how nonparametric, isotonic regression can be used to correct poorly
calibrated models for the said functional with applications in actuarial rate-making or similar predictive contexts. Furthermore, we relate the results to the recently developed isotonic distributional regression and distributional index models, pointing out how these procedures may enhance the typical actuarial toolkit for uncertainty quantification.

Vejleder: Munir Haibu
Censor:   Sören Möller, SDU