ArticleJournal of applied statistics2019
Loss functions in restricted parameter spaces and their Bayesian applications.
Article in Journal of applied statistics, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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Who cites it
6 citing papers in PubMed.
- Developing Bayesian EWMA chart for change detection in the shape parameter of Inverse Gaussian process.PloS one · 2024Article
- Improving safety of the continual reassessment method via a modified allocation rule.Statistics in medicine · 2020Article
- A flexible design for advanced Phase I/II clinical trials with continuous efficacy endpoints.Biometrical journal. Biometrische Zeitschrift · 2019Article
- A novel measure of drug benefit-risk assessment based on Scale Loss Score.Statistical methods in medical research · 2019Article
- An information theoretic phase I-II design for molecularly targeted agents that does not require an assumption of monotonicity.Journal of the Royal Statistical Society. Series C, Applied statistics · 2019Article
- A proposal for a new PhD level curriculum on quantitative methods for drug development.Pharmaceutical statistics · 2018Article
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Authors and funding
3 authors.
Funding
Abstract
Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to suboptimal solutions when a parameter is defined on a restricted space. It can also be an inappropriate choice in the context when an extreme overestimation and/or underestimation results in severe consequences and a more conservative estimator is preferred. We advocate a class of loss functions for parameters defined on restricted spaces which infinitely penalize boundary decisions like the squared error loss does on the real line. We also recall several properties of loss functions such as symmetry, convexity and invariance. We propose generalizations of the squared error loss function for parameters defined on the positive real line and on an interval. We provide explicit solutions for corresponding Bayes estimators and discuss multivariate extensions. Four well-known Bayesian estimation problems are used to demonstrate inferential benefits the novel Bayes estimators can provide in the context of restricted estimation.
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