A prior-free framework of coherent inference and its derivation of simple shrinkage estimators

DOI10.1016/j.jspi.2013.08.011zbMath1279.62068OpenAlexW2028437104WikidataQ57826609 ScholiaQ57826609MaRDI QIDQ393558

David R. Bickel, Marta Padilla

Publication date: 23 January 2014

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://biostats.bepress.com/cobra/art95

zbMATH Keywords

confidence measuresfiducial inferenceconfidence curvesconfidence distributionsconfidence posterior distributionsfiducial shrinkageobserved confidence levels

Mathematics Subject Classification ID

Parametric tolerance and confidence regions (62F25) Bayesian inference (62F15)

Related Items (11)

Confidence intervals, significance values, maximum likelihood estimates, etc. sharpened into Occam’s razors ⋮ Bayesian revision of a prior given prior-data conflict, expert opinion, or a similar insight: a large-deviation approach ⋮ Confidence distributions and empirical Bayes posterior distributions unified as distributions of evidential support ⋮ Maximum entropy derived and generalized under idempotent probability to address Bayes-frequentist uncertainty and model revision uncertainty: an information-theoretic semantics for possibility theory ⋮ Blending Bayesian and frequentist methods according to the precision of prior information with applications to hypothesis testing ⋮ Fiducialize statistical significance: transformingp-values into conservative posterior probabilities and Bayes factors ⋮ Inference after checking multiple Bayesian models for data conflict and applications to mitigating the influence of rejected priors ⋮ An Ensemble Kalman Filter Implementation Based on Modified Cholesky Decomposition for Inverse Covariance Matrix Estimation ⋮ Self-consistent confidence sets and tests of composite hypotheses applicable to restricted parameters ⋮ A note on fiducial model averaging as an alternative to checking Bayesian and frequentist models ⋮ Non-linear data assimilation via trust region optimization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fiducial prediction intervals
• Game-theoretic probability combination with applications to resolving conflicts between statistical methods
• Fiducial inference under nonparametric situations
• Empirical Bayes interval estimates that are conditionally equal to unadjusted confidence intervals or to default prior credibility intervals
• Generalised data augmentation and posterior inferences
• On construction of asymptotically correct confidence intervals
• The formal definition of reference priors
• Statistical decision theory and Bayesian analysis. 2nd ed
• Combining information from independent sources through confidence distributions
• The functional-model basis of fiducial inference
• What is a statistical model? (With comments and rejoinder).
• Inference rules and inferential distributions
• Controlling the degree of caution in statistical inference with the Bayesian and frequentist approaches as opposite extremes
• Mathematical foundations for a theory of confidence structures
• Reconciling Bayesian and frequentist evidence in the point null testing problem
• Shrinkage estimation of effect sizes as an alternative to hypothesis testing followed by estimation in high-dimensional biology: applications to differential gene expression
• The Dempster-Shafer calculus for statisticians
• Simple estimators of false discovery rates given as few as one or two \(p\)-values without strong parametric assumptions
• A frequentist framework of inductive reasoning
• Invariance of posterior distributions under reparametrization
• Confidence curves and improved exact confidence intervals for discrete distributions
• Estimators of the local false discovery rate designed for small numbers of tests
• Using confidence distribution sampling to visualize confidence sets
• Estimating the Null Distribution to Adjust Observed Confidence Levels for Genome-Scale Screening
• The Highest Confidence Density Region and Its Usage for Joint Inferences about Constrained Parameters
• Coherent Frequentism: A Decision Theory Based on Confidence Sets
• Some Problems Connected with Statistical Inference
• An Example of Wide Discrepancy Between Fiducial and Confidence Intervals
• Statistical Inference: Likelihood to Significance
• Model Selection and Model Averaging
• Shrinkage confidence intervals for the normal mean: Using a guess for greater efficiency
• Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence
• On Fiducial Inference
• The Uncertain Reasoner's Companion
• Confidence and Likelihood^*
• Bayes and likelihood calculations from confidence intervals
• Some Remarks on Pivotal Models and the Fiducial Argument in Relation to Structural Models
• Pivotal Models and the Fiducial Argument
• Principles of Statistical Inference
• Confidence Curves: An Omnibus Technique for Estimation and Testing Statistical Hypotheses
• Fiducial Generalized Confidence Intervals
• R. A. Fisher in the 21st century. Invited paper presented at the 1996 R. A. Fisher lecture. (With comments).

This page was built for publication: A prior-free framework of coherent inference and its derivation of simple shrinkage estimators