2020/04/01 by Samuel M. Fischer, Mark A. Lewis · 17 citations
Mathematics · #Advanced Statistical Methods and Models #Benchmark (surveying) #Confidence distribution #Confidence interval #Confidence region #Estimator #Expectation–maximization algorithm #Function (biology) #Likelihood function #Range (aeronautics) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #stat.CO
paper · pdf · doi:10.1007/s11222-021-10012-y
published in Statistics and Computing 31(4) (Springer Science+Business Media) · Keywords: computer algorithm; constrained optimization; parameter estimation; estimability; identifiability
arxiv created 2020/04/01 · openalex created_date 2020/04/10 · openalex publication_date 2021/05/07 · arxiv updated 2021/05/10 · openalex updated_date 2026/08/05
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.