Statistical Science

Larry Brown’s Contributions to Parametric Inference, Decision Theory and Foundations: A Survey

James O. Berger and Anirban DasGupta

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Abstract

This article gives a panoramic survey of the general area of parametric statistical inference, decision theory and foundations of statistics for the period 1965–2010 through the lens of Larry Brown’s contributions to varied aspects of this massive area. The article goes over sufficiency, shrinkage estimation, admissibility, minimaxity, complete class theorems, estimated confidence, conditional confidence procedures, Edgeworth and higher order asymptotic expansions, variational Bayes, Stein’s SURE, differential inequalities, geometrization of convergence rates, asymptotic equivalence, aspects of empirical process theory, inference after model selection, unified frequentist and Bayesian testing, and Wald’s sequential theory. A reasonably comprehensive bibliography is provided.

Article information

Source
Statist. Sci., Volume 34, Number 4 (2019), 621-634.

Dates
First available in Project Euclid: 8 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.ss/1578474028

Digital Object Identifier
doi:10.1214/19-STS717

Mathematical Reviews number (MathSciNet)
MR4048594

Keywords
Admissibility ancillary asymptotic equivalence Bayes conditional confidence differential inequality Edgeworth expansions estimated confidence minimax sequential shrinkage sufficiency

Citation

Berger, James O.; DasGupta, Anirban. Larry Brown’s Contributions to Parametric Inference, Decision Theory and Foundations: A Survey. Statist. Sci. 34 (2019), no. 4, 621--634. doi:10.1214/19-STS717. https://projecteuclid.org/euclid.ss/1578474028


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