Larry Brown's contributions to parametric inference, decision theory and foundations: a survey

DOI10.1214/19-STS717zbMath1440.62003OpenAlexW2998904400MaRDI QIDQ2194579

James O. Berger, Anirban DasGupta

Publication date: 26 August 2020

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ss/1578474028

zbMATH Keywords

minimaxBayesdifferential inequalityEdgeworth expansionsshrinkageadmissibilitysequentialsufficiencyasymptotic equivalenceancillaryconditional confidenceestimated confidence

Mathematics Subject Classification ID

Bayesian inference (62F15) Foundations and philosophical topics in statistics (62A01) History of statistics (62-03) General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics (62-00) General considerations in statistical decision theory (62C05)

Related Items

Larry Brown's work on admissibility

Cites Work

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• Valid post-selection inference
• A heuristic method for determining admissibility of estimators - with applications
• Information inequalities for the Bayes risk
• The admissibility of the Kaplan-Meier and other maximum likelihood estimators in the presence of censoring
• Admissibility, difference equations and recurrence in estimating a Poisson mean
• A sharp necessary condition for admissibility of sequential tests - necessary and sufficient conditions for admissibility of SPRT's
• A conversation with Larry Brown
• Minimax risk over hyperrectangles, and implications
• Admissible estimators of binomial probability and the inverse Bayes rule map
• Statistical decision theory and Bayesian analysis. 2nd ed
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• Monotonicity of Bayes sequential tests
• A stepwise Bayesian procedure
• A complete class theorem for statistical problems with finite sample spaces
• Estimation of the mean of a multivariate normal distribution
• Minimax estimation of the mean of a normal distribution when the parameter space is restricted
• Inadmissibility of large classes of sequential tests
• Natural exponential families with quadratic variance functions
• Information inequality bounds on the minimax risk (with an application to nonparametric regression)
• Estimated confidence under the validity constraint
• A statistical diptych: Admissible inferences -- recurrence of symmetric Markov chains
• Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss
• Minimax estimation of a normal mean vector for arbitrary quadratic loss and unknown covariance matrix
• A contribution to Kiefer's theory of conditional confidence procedures
• Admissible and minimax estimation for the multinomial distribution and for k independent binomial distributions
• Asymptotic equivalence of nonparametric regression and white noise
• Asymptotic equivalence of density estimation and Gaussian white noise
• Interval estimation for a binomial proportion. (With comments and a rejoinder).
• Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift
• Density estimation by wavelet thresholding
• Choice of hierarchical priors: Admissibility in estimation of normal means
• Confidence intervals for a binomial proportion and asymptotic expansions
• A unified conditional frequentist and Bayesian test for fixed and sequential simple hypothesis testing
• Nonexistence of informative unbiased estimators in singular problems
• The heat equation and Stein's identity: connections, applications
• Measurable selections of extrema
• An ancillarity paradox which appears in multiple linear regression
• The Admissibility of Pitman's Estimator of a Single Location Parameter
• On independent statistical decision problems and products of diffusions
• CAN ONE ESTIMATE THE UNCONDITIONAL DISTRIBUTION OF POST-MODEL-SELECTION ESTIMATORS?
• Admissibility of generalized bayes and pitman estimates in the non-regular family
• A Comparison of Some Approximate Confidence Intervals for the Binomial Parameter
• Binomial Confidence Intervals
• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• Simultaneous Estimation of the Means of Independent Poisson Laws
• Conditional Confidence Statements and Confidence Estimators
• Bounds on the Bayes and minimax risk for signal parameter estimation
• An Essay on Statistical Decision Theory
• Admissibility: Survey of a Concept in Progress
• Admissibility for Estimation with Quadratic Loss
• Sufficiency Statistics in the Case of Independent Random Variables
• Testing Statistical Hypotheses
• On the Admissibility of Invariant Estimators of One or More Location Parameters
• The Conditional Level of Student's $t$ Test
• Estimates of Linear Combinations of the Parameters in the Mean Vector of a Multivariate Distribution
• Admissible Estimators, Recurrent Diffusions, and Insoluble Boundary Value Problems
• On the Admissible Estimators for Certain Fixed Sample Binomial Problems
• A Lower Bound for the Risk in Estimating the Value of a Probability Density
• Application of the Radon-Nikodym Theorem to the Theory of Sufficient Statistics
• On the Translation Parameter Problem for Discrete Variables
• An Essentially Complete Class of Decision Functions for Certain Standard Sequential Problems
• The Admissibility of Certain Invariant Statistical Tests Involving a Translation Parameter
• Sufficiency and Statistical Decision Functions
• Sequential Tests of Statistical Hypotheses
• Introduction to nonparametric estimation