Asymptotics in Statistics–Some Basic Concepts

By T. N. Sriram. 2002

723 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

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Citations in the corpus

Finite Sample Bernstein -- von Mises Theorem for Semiparametric Problems (2013, methodology): “The classical version of the BvM Theorem is stated for the standard parametric setup with a fixed parametric model and large samples; see Le Cam and Yang (1990); van der Vaart (2000) for a detailed overview.”
On Choosing and Bounding Probability Metrics (2002, background): “Le Cam and Yang (1990) and Liese and Vajda (1987) contain further historical references.”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, background): “The Fisher information bound [35] for the parameter θ 0 is M loc n ( P θ 0 , L sq , P , { id } ) More generally, if we wish to estimate a functional θ ( P ) ∈ R of a distribution P , Donoho and Liu [16, 17, 18] show how the modulus of continuity takes the place of the classical information bound.”
The Bernstein-Von-Mises theorem under misspecification (2012, methodology): “A version of the theorem involving only first derivatives of the log-likelihood in combination with testability and prior mass conditions (compare with Schwartz’ consistency theorem, Schwartz (1965) [16]) can be found in Van der Vaart (1998) [18] which copies (and streamlines) the approach Le Cam pr”
Asymptotic equivalence for nonparametric regression (2024, positive): “The abovementioned results are part of an eﬀort to extend Le Cam’s asymptotic theory (see Le Cam [12] and Le Cam and Yang [13]) to a class of general models with inﬁnite dimensional parameters which cannot be estimated at the usual ”root-n ” rate n − 1 / 2 .”