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Larry Brown’s contributions to parametric inference, decision theory and foundations: a survey. (English) Zbl 1440.62003
Summary: 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 L. Brown’s [Fundamentals of statistical exponential families with applications in statistical decision theory. Hayward, CA: Institute of Mathematical Statistics (1986; Zbl 0685.62002); J. Am. Stat. Assoc. 95, No. 452, 1277–1281 (2000; Zbl 1009.62502)] 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.
MSC:
62-03 History of statistics
62F15 Bayesian inference
62C05 General considerations in statistical decision theory
62A01 Foundations and philosophical topics in statistics
62-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics
Biographic References:
Brown, Lawrence David
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References:
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