Theory of point estimation

By Eric R. Ziegel, Erich Leo Lehmann, George Casella. 1950

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Optimal Schemes for Discrete Distribution Estimation Under Locally Differential Privacy (2017, methodology): “n-private) distribution estimation problem, we are given direct access to i.i.d. samples tXpiqun i“1 drawn according to some unknown distribution p P ∆k.Our goal is to estimate p based on the samples [6]. We deﬁne an estimator ˆp as a function ˆp : Xn Ñ Rk,and assess the quality of the estimator ˆp ”
Discrete Distribution Estimation under Local Privacy (2016, background): “These same mechanisms may also be applied to closed alphabets known a priori.”
All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, methodology): “The mean, variance, and asymptotic distribution of the estimator M̂Rdifference(f) := êswitch(f)− êorig(f) can be easily determined using results for U-statistics, without the use of the delta method (Dorfman, 1938; Lehmann and Casella, 2006; see also Ver Hoef, 2012).”
Minimax Estimation of Kernel Mean Embeddings (2016, background): “ional, i.e., Hk= Rd. For a distribution P on Rd satisfying R Rdkxk2 dP(x) <∞, this choice of kernel yields µP = R xdP(x) as the mean embedding of P which simply is the mean of P. It is well-known (Lehmann and Casella, 2008, Chapter 5, Example 1.14) that the minimax rate of estimating µP ∈ Rd base”
Kernel Mean Estimation and Stein's Effect (2013, neutral): “Several discussions supporting this argument can be found in [13, 4].”
Variance-based Regularization with Convex Objectives (2016, methodology): “van der Vaart and Wellner [47] or Lehmann and Casella [29]), which proceed by performing a Taylor expansion of the objective in a neighborhood of the optimum and using local asymptotic normality arguments.”
Learning to Optimize via Posterior Sampling (2013, background): “as in Agrawal and Goyal [5], but should instead place more prior weight on the worst possible realizations of (see the discussion of \least favorable" prior distributions in Lehmann and Casella [27]). 3.2. On Changing Action Sets. Our stochastic model of action sets A t is distinct relative to ”
NSML: Meet the MLaaS platform with a real-world case study (2018, methodology): “The former one is a kind of regression task, thus mean squared error (Lehmann & Casella, 1998) was chosen as an evaluation metric.”
Explicit Inductive Bias for Transfer Learning with Convolutional Networks (2018, background): “Shrinking towards zero is the most common form of shrinkage, but shrinking towards adaptively chosen targets has been around for some time, starting with Stein shrinkage (see e.g. Lehmann & Casella 1998, chapter 5), and more recently with SVM.”
Minimax Estimation of Functionals of Discrete Distributions (2014, unknown): “ry community, and deeply embedded in fundamental concepts of various disciplines. Below we name a few related applications. In statistics, one of the popular criterion for objective Bayesian modeling [9] is to design a prior on the parameter to maximize the mutual information between the parameter a”
A theory of robust long-run variance estimation (2007, background): “In many empirical applications, little is known about the dynamic properties of T1=2DuT ;t in (1).”
Principles of Statistical Inference (2006, background): “Lehmann which have acquired coauthors as successive revisions have been produced (Lehmann and Casella, 2001; Lehmann and Romano, 2004).”
The Step Decay Schedule: A Near Optimal, Geometrically Decaying Learning Rate Procedure (2019, background): “(2017b)): Towards statistically optimal estimation procedures: The goal of this line of thought is to match the excess risk of the statistically optimal estimator (Anbar, 1971; Kushner and Clark, 1978; Polyak and Juditsky, 1992; Lehmann and Casella, 1998) on every problem instance.”
Additive nonlinear biomass equations: A likelihood-based approach (2016, methodology): “Under standard conditions, the ML parameter estimators are asymptotically Gaussian distributed with variance-covariance matrix given by the inverse of the Fisher information matrix (Lehmann and Casella 1998, §6.3).”
Information Geometry of the Gaussian Distribution in View of Stochastic Optimization (2015, background): “3 (b) in [18], and in particular when log p(x;ξ) is twice differentiable, the Fisher information matrix can be obtained by taking the negative of the expected value of the second derivative of the score, that is,”