Asymptotic Methods In Statistical Decision Theory

By Lucien Le Cam. 1986

How researchers see this paper

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

Citations in the corpus

Bayesian Model-Agnostic Meta-Learning (2018, positive): “…et al. (2018), the task-train posterior of a Bayesian neural network (BNN) trained with a few-shot dataset would have a signiﬁcant amount of uncertainty which, according to the Bayesian central limit theorem (Le Cam, 1986; Ahn et al., 2012), cannot be well approximated by a Gaussian distribution.”
Stochastic Gradient Descent as Approximate Bayesian Inference (2017, background): “Assume that the sample size N is large enough that the Bernstein-von Mises theorem (Le Cam, 1986) applies (hence the posterior is Gaussian).”
Bayesian Posterior Sampling via Stochastic Gradient Fisher Scoring (2012, neutral): “This is formalized by the Bernstein-von Mises theorem, a.k.a the Bayesian Central Limit Theorem, (Le Cam, 1986), which states that under suitable regularity conditions, p ( θ | { x 1 ...x N } ) approximately equals N ( θ 0 , I − 1 N ) as N becomes very large.”
On Choosing and Bounding Probability Metrics (2002, methodology): “Some texts, e.g., LeCam (1986), introduce a factor of a square root of two in the deﬁnition of the Hellinger distance to normalize its range of possible values to [0 , 1].”
Tensor decompositions for learning latent variable models (2012, neutral): “L G ]”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, background): “Indeed, Le Cam’s theory of quadratic mean diﬀerentiability, contiguity, local asymptotic normality, and local alternatives for testing all reposes on closeness in Hellinger distance [34, 35, 42, 50], which justiﬁes the use of Fisher Information in classical statistical problems.”
SEMIPARAMETRICALLY EFFICIENT RANK-BASED INFERENCE FOR SHAPE II. OPTIMAL R-ESTIMATION OF SHAPE (2006, unknown): “4 in [30] for a typical use), are quite standard in Le Cam’s onestep construction of estimators (see [31]), and several of them, characterized by a # subscript, will appear in the sequel.”
Convergence rates of posterior distributions (2000, background): “For the latter see e.g. Le Cam (1986), Proposition 2 on p483.”
On Non‐parametric Testing, the Uniform Behaviour of the t‐test, and Related Problems (2004, methodology): “The total variation metric s is well known and has many statistical uses (see Le Cam, 1986, Chapter 4).”
Semiparametric Minimax Rates (2009, background): “See [5], [4] page 47, or [1] Corollary 1.”
Inverse problems as statistics (2002, methodology): “The description here is based in part on Lehmann and Casella [47, chapter 4]; see Hartigan [38] and Berger [11] for more complete and technical expositions of the Bayesian approach,Gelman et al [35] for Bayesian data analysis and Le Cam [44] for a more general and rigorous development.”
Asymptotically Exact, Embarrassingly Parallel MCMC (2013, methodology): “The ﬁrst method for forming samples from the full posterior given subposterior samples involves using an approximation based on the Bernstein-von Mises (Bayesian central limit) theorem, an important result in Bayesian asymptotic theory.”
How many bins should be put in a regular histogram (2006, methodology): “Let us just briefly mention that˜f 2 and˜f 3 are respectively L 2 and Kullback-Leibler cross-validation methods, ˜ f 4 is the minimization of AIC, ˜ f 5 and˜f 6 are based on stochastic complexity and minimum description length respectively, ˜ f 7 tõ f 10 are estimators based on asymptotic evaluation”
Asymptotic nonequivalence of GARCH models and di?usions (2002, methodology): “Our approach to proving the theorems is based on the following principle described in Le Cam (1986), Le Cam and Yang (1990) and Nussbaum (1996). For two experiments IEi = ( i;Fi; (Pi; ; 2 )), i = 1; 2, assume there is some 2 such that all the Pi; are dominated by Pi; , i = 1; 2, and form i( ) = dPi;”
On Measures of Entropy and Information (2015, background): “LeCam divergence (LeCam discrimination, VinczeLeCam divergence, triangular divergence) [39, 40]”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, methodology): “The beautiful theory of Hájek and Le Cam [11]–[13] shows that, as the number of observed samples grows without bound while the finite parameter dimension (e.”
Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics (2014, background): “xœRp f (x) Theorem (Performance of the ML estimator [36, 65]) The random variable ˆ xML satisfies”