INADMISSIBILITY OF THE USUAL ESTIMATOR FOR THE MEAN OF A MULTIVARIATE NORMAL DISTRIBUTION

By Jerzy Neyman. 2005

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In Statistics and Probability

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Inspired by the James-Stein estimator of the mean of multivariate Gaussian distribution (Stein 1955, James and Stein 1961), Muandet et al. (2014a; 2016) proposed a shrinkage estimator of the kernel mean which has the form µ̂α := αf∗ + (1− α)µ̂P, (3.22) for some f∗ ∈ H which is independent of the…”
Nonparametric Independence Testing for Small Sample Sizes (2014, methodology): “We provide evidence that employing shrunk estimators of ΣXY , instead of SXY , to calculate the aforementioned test statistic, can increase the power of the associated independence test at low false positive rates, when the sample size is small (there is higher variance in estimating…”
Kernel Mean Shrinkage Estimators (2014, methodology): “This work is to some extent inspired by Stein’s seminal work in 1955, which showed that the maximum likelihood estimator (MLE) of the mean, θ of a multivariate Gaussian distribution N ( θ, σ 2 I ) is “inadmissible” (Stein, 1955)— i.e. , there exists a better estimator—though it is minimax optimal.”
Kernel Mean Estimation and Stein's Effect (2013, positive): “Charles Stein showed in 1955 that it is possible to uniformly improve the maximum likelihood estimator (MLE) for the Gaussian model in terms of total squared error risk when several parameters are estimated simultaneously from independent normal observations [14].”
Continuous Meta-Learning without Tasks (2019, methodology): “We also note that maximum likelihood estimation of Gaussian means is dominated by the James-Stein estimator (Stein, 1956), which shrinks the least squares estimator toward some prior.”
Multi-Task Learning as Multi-Objective Optimization (2018, background): “Stein (1956) showed that it is better to estimate the means of three or more Gaussian random variables using samples from all of them rather than estimating them separately, even when the Gaussians are independent.”
Bayesian mixed-effects inference on classification performance in hierarchical data sets (2012, background): “For early contributions to the extensive literature on shrinkage effects, see Stein (1956), James and Stein (1961), and Efron and Morris (1971, 1972).”
Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach (2004, unknown): “algorithms for solving max-min saddle-point problems numerically and apply the algorithms to portfolio choice problem, while Wang (2005) shows how to obtain the optimal portfolio numerically in a Bayesian setting in the presence of aversion to model uncertainty.”
Conflict-Averse Gradient Descent for Multi-task Learning (2021, background): “Moreover, it has been shown that MTL could in principle improve the quality of the learned representation and therefore benefit individual tasks [35, 43, 34].”
Cleaning large correlation matrices: tools from random matrix theory (2016, background): “Even though the Wishart distribution gives us many important properties concerning E, the behavior of the sample estimator as a function of N was understood much later with the pioneering work of Charles Stein in 1956 [10].”
Learning Populations of Parameters (2017, background): “This ability to “denoise” the empirical estimate of a parameter based on the observations of a number of independent random variables (in this case, the outcomes of the tosses of the other coins), was first pointed out by Charles Stein in the setting of estimating the means of a set of Gaussians and”
Return of the Phantom Menace (2009, background): “…(Mallows, 1973), information theoretic model selection criteria such as AIC (Akaike, 1973) and BIC (Schwarz, 1978), Stein-like shrinkage estimators (Stein, 1955), various nonnested tests (Cox, 1961; Vuong, 1989; Clarke, 2001; Clarke, 2003; Clarke, 2007), and econometric methodologies such as the…”
Dynamic Linear Models with R (2009, unknown): “Stein (1956) proved that, if n ≥ 3, there exists another estimator θ∗ = θ∗(Y ) which”
Prior Selection for Vector Autoregressions (2015, unknown): “It is well known, however, that working with flat priors leads to inadmissible estimators (Stein, 1956) and yields poor inference, particularly in large-dimensional systems (see, e.”
A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing * (2003, background): “But what if you had never heard of Stein (1955) or the rest of the literature, and you just naively fit the simple model?”
Minimax Estimation of Functionals of Discrete Distributions (2014, background): “The seminal work of Stein [32] revealed the famous Stein’s phenomenon that uniformly minimum variance unbiased estimators could be inadmissible, i.”