Constructing confidence intervals of extreme rainfall quantiles using Bayesian, bootstrap, and profile likelihood approaches

2015 ◽  
Vol 59 (4) ◽  
pp. 573-585 ◽  
Author(s):  
Si Chen ◽  
YaXing Li ◽  
JiYae Shin ◽  
TaeWoong Kim
Keyword(s):  
Confidence Intervals ◽  
Profile Likelihood ◽  
Extreme Rainfall ◽  
Bayesian Bootstrap

scholarly journals Efficient profile-likelihood confidence intervals for capture-recapture models

2005 ◽  
Vol 10 (2) ◽  
pp. 184-196 ◽  
Author(s):  
Olivier Gimenez ◽  
Rémi Choquet ◽  
Laurent Lamor ◽  
Paul Scofield ◽  
David Fletcher ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Profile Likelihood ◽  
Capture Recapture

scholarly journals Construction of confidence intervals for extreme rainfall quantiles

2012 ◽  
Author(s):  
A. T. Silva ◽  
M. M. Portela ◽  
J. Baez ◽  
M. Naghettini
Keyword(s):  
Confidence Intervals ◽  
Extreme Rainfall

scholarly journals A robust and efficient algorithm to find profile likelihood confidence intervals

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Samuel M. Fischer ◽  
Mark A. Lewis
Keyword(s):  
Confidence Intervals ◽  
Likelihood Function ◽  
Profile Likelihood ◽  
Asymptotic Properties ◽  
Trust Region ◽  
Benchmark Problems ◽  
Success Rates ◽  
Wide Range ◽  
Local Approximations ◽  
Model Predictions

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.

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