Abstract
AbstractProfile 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.
Funder
Canadian Aquatic Invasive Species Network
Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
Canada Excellence Research Chairs, Government of Canada
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Statistics, Probability and Uncertainty,Statistics and Probability,Theoretical Computer Science
Reference34 articles.
1. Akrami, Y., Scott, P., Edsjö, J., Conrad, J., Bergström, L.: A profile likelihood analysis of the constrained MSSM with genetic algorithms. J. High Energy Phys. 2010(4), 57 (2010)
2. Albertsen, C.M., Whoriskey, K., Yurkowski, D., Nielsen, A., Flemming, J.M.: Fast fitting of non-Gaussian state-space models to animal movement data via Template Model Builder. Ecology 96(10), 2598–2604 (2015)
3. Brodtkorb, P.A., D’Errico, J.: numdifftools 0.9.39. Retrieved from https://github.com/pbrod/numdifftools (2019)
4. Buckland, S.T.: Monte Carlo confidence intervals. Biometrics 40(3), 811 (1984)
5. Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. MPS-SIAM series on optimization. Society for Industrial and Applied Mathematics, Philadelphia (2000)
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献