Estimation with Quadratic Loss

By W. James, C. Stein. 1992

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistical Learning Theory

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…”
Computing functions of random variables via reproducing kernel Hilbert space representations (2015, positive): “ean of the empirical distribution) m[pˆ m]= 1 m m å i=1 F(x i)= m[X]; (17) where X = fx 1;:::;x mgis an i.i.d. sample from p (cf. (10)). As an aside, note that using ideas from James-Stein estimation [17], we can construct shrinkage estimators that improve upon the standard empirical estimator (see ”
Kernel Mean Shrinkage Estimators (2014, methodology): “While the proposed estimators in Section 2.2 and 2.3 are theoretically interesting, they are not useful in practice as they require the knowledge of the true data generating distribution.”
Kernel Mean Estimation and Stein's Effect (2013, positive): “Perhaps the best known estimator of such kind is James-Stein’s estimator [15].”
Proportion of non‐zero normal means: universal oracle equivalences and uniformly consistent estimators (2008, background): “The oracle equivalence reduces the problem of estimating the proportion to the problem of estimating the oracle, while the latter is relatively easier to handle.”
Small Area Shrinkage Estimation (2012, background): “In addition, if instead of the posterior mean, one estimates B by its posterior mode, one gets the estimator B̂MO =min((m− p− 4)V/S,1), which leads to an estimator of θ quite akin to the positive part James–Stein estimator, the only difference being that m− p− 2 is now replaced by m− p− 4.”
Information-theoretic metric learning (2006, background): “The LogDet divergence is also known as Stein s loss, having originated in the work of (James & Stein, 1961).”
Sub-Gaussian estimators of the mean of a random vector (2017, background): “…X i has a mean squared error equal to Tr( Σ ) /N (where Tr( Σ ) denotes the trace of the covariance matrix) and, even though this estimator is not necessarily optimal even for standard normal vectors—by “Stein’s paradox”, see [10]—, the order of magnitude of the error cannot be improved in general.”
Sequential Covariance-Matrix Estimation with Application to Mitigating Catastrophic Forgetting (2015, methodology): “This is an application of the general shrinkage principle, going back to [14], [15].”
Review of "Mining the Web: discovering knowledge from hypertext data" by Soumen Chakrabati. Morgan Kaufman 2003. (2002, unknown): “Shrinkage as a general statistical tool has been discussed by Carlin, Louis, James and Stein [33, 198, 110].”
Decision Theory Applied to an Instrumental Variables Model (2007, methodology): “There is an even simpler model, a version of the k-means model of Stein (1956, 1959) and James and Stein (1961), in which the parameters consist of the scalar ρ and the point ω on the unit sphere with dimension (k − 1).”
Shrinkage Estimation of Regression Coefficients From Censored Data With Multiple Observations (2001, background): “Th e shrinkage estimator (SE) (Stein, 1956; James and Stein, 1961 ) is de fined by”