Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1007/s11222-021-10012-y
Licence creative commons licence
Title (Primary) A robust and efficient algorithm to find profile likelihood confidence intervals
Author Fischer, S.M. ORCID logo ; Lewis, M.A.
Journal Statistics and Computing
Year 2021
Department OESA
Volume 31
Issue 4
Page From art. 38
Language englisch
Topic T5 Future Landscapes
Keywords Computer algorithm; Constrained optimization; Parameter estimation; Estimability; Identifiability
Abstract +Profile likelihood confidence intervals are a robust alternative to Wald’s method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood confidence intervals can be difficult to solve in these situations, because the likelihood function may exhibit unfavorable properties. As a result, existing methods may be inefficient and yield misleading results. In this paper, we address this problem by computing profile likelihood confidence intervals via a trust-region approach, where steps computed based on local approximations are constrained to regions where these approximations are sufficiently precise. As our algorithm also accounts for numerical issues arising if the likelihood function is strongly non-linear or parameters are not estimable, the method is applicable in many scenarios where earlier approaches are shown to be unreliable. To demonstrate its potential in applications, we apply our algorithm to benchmark problems and compare it with 6 existing approaches to compute profile likelihood confidence intervals. Our algorithm consistently achieved higher success rates than any competitor while also being among the quickest methods. As our algorithm can be applied to compute both confidence intervals of parameters and model predictions, it is useful in a wide range of scenarios.
Persistent UFZ Identifier
Fischer, S.M., Lewis, M.A. (2021):
A robust and efficient algorithm to find profile likelihood confidence intervals
Stat. Comput. 31 (4), art. 38