Stein's Paradox in Statistics

By Bradley Efron, Carl N. Morris. 1977

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Citations in the corpus

Kernel Mean Shrinkage Estimators (2014, background): “This ﬁnding is quite remarkable as it is counter-intuitive as to why joint estimation should yield better estimators when all parameters are mutually independent (Efron and Morris, 1977).”
Fitting Linear Mixed-Effects Models Using lme4 (2014, methodology): “For example, the random-effects implementation of such interactions can be used to obtain shrinkage estimates of regression coefficients (e.g., Efron and Morris 1977), or account for lack of independence in the residuals due to block structure or repeated measurements (e.g., Laird and Ware 1982).”
On parametric empirical Bayes methods for comparing multiple groups using replicated gene expression profiles (2003, methodology): “Empirical Bayes methods provide a natural approach to microarray data analysis because they can signi cantly reduce the dimensionality of an inference problem involving many unknown parameters (for example, Efron and Morris [3, 4]).”
Multi-Task Averaging (2011, methodology): “The most closely related work is Stein estimation, an empirical Bayes strategy for estimating multiple means simultaneously [7, 8, 2, 9].”
Absolute identification by relative judgment. (2005, background): “Instead, estimates derived by shrinking each observation toward the grand mean of all the observations are better.4 Efron and Morris (1977) provided an accessible introduction to James–Stein estimators and gave the example of baseball players: The best estimate of a player’s batting average in the…”
Learning Neural Networks with Adaptive Regularization (2019, methodology): “, the James-Stein estimator [23] and the Efron-Morris estimator [11], dominate the classic maximum likelihood estimator (MLE) in terms of quadratic loss for every choice of the model parameter w.”
Improved estimation of the covariance matrix of stock returns with an application to portfolio selection (2003, background): “Efron and Morris (1977) provide a general introduction to shrinkage, and Jorion (1986) shows its importance in the context of portfolio selection.”
Sample size for binary logistic prediction models: Beyond events per variable criteria (2018, background): “In most circumstances shrinkage estimators can be defined that have lower expected error for estimating probabilities in new individuals than ML estimators.(30,31) The benefits of the shrinkage estimators over the corresponding ML estimators decreases with increasing EPV.”
Bayesian Analysis of Factorial Designs (2017, methodology): “Shrinkage estimators are well known in both Bayesian and frequentist statistical literatures (e.g., Efron & Morris, 1977; James & Stein, 1961), and in most situations are more accurate than sample means (Stein, 1959).”
Hierarchical generalized additive models in ecology: an introduction with mgcv (2019, background): “Penalization is useful because using a penalty term slightly increases model bias, but can substantially decrease variance ( Efron & Morris, 1977 ).”
Centre De Referència En Economia Analítica Barcelona Economics Working Paper Series Working Paper Nº 92 Honey, I Shrunk the Sample Covariance Matrix Honey, I Shrunk the Sample Covariance Matrix (unknown): “An excellent non-technical primer on shrinkage using real-life examples of baseball batting averages was written by Efron and Morris (1977).”