Profile Likelihood via Optimisation and Differential Equations Article Swipe
Profile likelihood provides a general framework to infer on a scalar parameter of a statistical model. A confidence interval is obtained by numerically finding the two abscissas where the profile log-likelihood curve intersects an horizontal line. An alternative derivation for this interval can be obtained by solving a constrained optimisation problem which can broadly be described as: maximise or minimise the parameter of interest under the constraint that the log-likelihood is high enough. This formulation allows nice geometrical interpretations; It can be used to infer on a parameter or on a known scalar function of the parameter, such as a quantile. Widely available routines for constrained optimisation can be used for this task, as well as Markov Chain Monte Carlo samplers. When the interest is on a smooth function depending on an extra continuous variable, the constrained optimisation framework can be used to derive Ordinary Differential Equation (ODE) for the confidence limits. This is illustrated with the return levels of Extreme Value models based on the Generalised Extreme Value distribution. Moreover the same ODE-based technique applies as well to the derivation of profile likelihood contours for couples of parameters. The initial value of the ODE used in the determination of the interval or the contour can itself be obtained by another auxiliary ODE with known initial value obtained by using the confidence level as the extra continuous variable.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2404.02774
- https://arxiv.org/pdf/2404.02774
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4393969114
All OpenAlex metadata
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https://openalex.org/W4393969114Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2404.02774Digital Object Identifier
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Profile Likelihood via Optimisation and Differential EquationsWork title
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preprintOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-04-03Full publication date if available
- Authors
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Yves DevilleList of authors in order
- Landing page
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https://arxiv.org/abs/2404.02774Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2404.02774Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2404.02774Direct OA link when available
- Concepts
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Applied mathematics, Differential (mechanical device), Computer science, Mathematics, Econometrics, Economics, Physics, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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