Stein's Estimation Rule and Its Competitors- An Empirical Bayes Approach

By Bradley Efron, Carl N. Morris. 1973

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Citations in the corpus

Bayesian Learning of Kernel Embeddings (2016, methodology): “Connections between the James-Stein estimator and empirical Bayes procedures are classical (Efron and Morris, 1973), and thus a natural question to consider is whether a Bayesian formulation of the problem of kernel embedding estimation would yield similar shrinkage properties. In this paper, we wil”
Continuous Meta-Learning without Tasks (2019, methodology): “Moreover, the James-Stein estimator paired with empirical Bayesian estimation of the prior—which is the basis for Bayesian meta-learning approaches such as ALPaCA and PCOC—has been shown to be a very effective estimator in this problem setting (Efron & Morris, 1973).”
Item Response Theory—A Statistical Framework for Educational and Psychological Measurement (2021, unknown): “This estimator can be viewed as an empirical Bayes estimator (Efron and Morris, 1973; Robbins, 1956); see Efron (2003) and Zhang (2003) for a review of empirical Bayes methods.”
A unified jackknife theory for empirical best prediction with M-estimation (2002, methodology): “The model parameter B can be unbiasedly estimated by B̂ = (m − 2)/∑mi=1 Y 2i [Efron and Morris (1973)].”
Small Area Shrinkage Estimation (2012, background): “Stein’s estimators gained immense popularity in the 1970s when Efron and Morris, in a series of articles, gave interesting EB interpreta- tion of these estimators (see, e.g., Efron and Morris, 1973).”
General maximum likelihood empirical Bayes estimation of normal means (2009, background): “The second approach, conceived with the celebrated Stein’s proof of the inadmissibility of the optimal unbiased estimator and the introduction of the James–Stein estimator [22, 31], is best understood through its parametric or linear EB interpretations [16, 17, 26].”
Bayesian model reduction and empirical Bayes for group (DCM) studies (2016, methodology): “In this paper, we will consider an empirical Bayesian approach to any hierarchical model that can be expressed in terms of an arbitrary (nonlinear) model at the first level and a standard (parametric) empirical Bayesian (PEB) model at higher levels (Efron and Morris, 1973; Kass and Steffey, 1989).”
Estimation of Finite Population Domain Means (2006, methodology): “…methods include the Bayesian method (e.g., Ericson 1969; Scott and Smith 1969; Datta and Ghosh 1991, among others), empirical Bayes method (e.g., Efron and Morris 1973; Morris 1983; Ghosh and Meeden 1986; Ghosh and Lahiri 1987; Arora, Lahiri, and Mukherjee 1997), and empirical best prediction…”
Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean (2015, methodology): “Then, as presented, for example, by Jiang and Zhang (2009), for a separable estimator with θ̂i = t(Xi), Rn(θ, θ̂) = n∑ i=1 1 n Eθi[t(Xi) − θi]2 = E[t(Y ) − ξ ]2 (4) where the expectation in the last term is taken over the pair (Y, ξ ) of random variables jointly distributed according to ξ ∼ 1 n n∑…”