Local asymptotic minimax and admissibility in estimation

By J. Hájek. 1972

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Citations in the corpus

Geometric Lower Bounds for Distributed Parameter Estimation Under Communication Constraints (2018, background): “When there is no communication constraints, classical Hájek–Le Cam theory Hájek (1972) tells that we can achieve a squared ℓ2 risk 1/(nI0) asymptotically for each coordinate, which sums up to d/(nI0) for the entire vector.”
Efficiently Breaking the Curse of Horizon in Off-Policy Evaluation with Double Reinforcement Learning (2019, methodology): “In the parametric iid setting, the seminal work of H´ajek (1970, 1972) shows that the CR bound (times n ) is also a lower bound on the asymptotic MSE of any regular estimator, or of any estimator almost everywhere, or of any estimator in some vanishing neighborhood of θ 0 (van der Vaart, 1998,…”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, background): “H´ajek local asymptotic minimax theory [26, 32, 34, 50, 35] cleanly delineates eﬃcient from ineﬃcient estimators in classical statistics and highlights the importance of local notions of optimality (making Fisher information bounds rigorous).”
On Adaptive Estimation in Nonstationary Arma Models with Garch Errors (2003, background): “In LAN models, Hájek (1972), Fabian and Hannan (1982) and Koul and Schick (1997) established the precise notion of efficiency.”
Minimax Estimation of Functionals of Discrete Distributions (2014, background): “14] in the sense of the Hájek convolution theorem [17] and the Hájek–Le Cam local asymptotic minimax theorem [18].”
Statistical inference for ergodic point processes and application to Limit Order Book (2015, methodology): “We refer the reader to [14,18], Sections II.”
Martingale transforms goodness-of-fit tests in regression models (2004, background): “= 〈α,mθ 〉v+ ρn(v), where under the assumed conditions and using an argument similar to one used, for example, in Hájek and Šidák (1967) one can show that sup‖v‖≤k |ρn(v)|= op(1).”
X-DIFFERENCING AND DYNAMIC PANEL MODEL ESTIMATION (2013, unknown): “The usual Hájek-Le Cam representation theory (Hájek, 1972; Le Cam, 1972) holds for locally asymptotically normal (LAN) families and regular estimators in the context of single index and √ n asymptotics.”
Minimax Estimation of Discrete Distributions Under $\ell _{1}$ Loss (2014, unknown): “Regarding the lower bound, the well-known Hájek-Le Cam local asymptotic minimax theorem [13] (Theorem 6 in Appendix A) and corresponding achievability theorems [2, Lemma 8.”
Fisher Information Under Local Differential Privacy (2020, methodology): “More generally, Fisher information describes the complexity of estimation problems in an asymptotic sense locally around θ [9], [10]; and a Bayesian version of the Cram´er-Rao bound known as the van Trees inequality can be used to give lower bounds that hold for any estimator (including arbitrarily…”
Efficiency improvements in inference on stationary and nonstationary fractional time series (2004, background): “MR1061950 [12] Hájek, J. (1972).”
The semiparametric Bernstein-von Mises theorem (2010, background): “The asymptotic minimax theorem (Hájek [18]) underlines the central role of the concept of regularity.”
Asymptotically optimal private estimation under mean square loss (2017, methodology): “1) Proof of (57): In order to prove inequality (57), we develop a refined version of the Local Asymptotic Normality approach [16], [17](2).”
A Tutorial on Fisher Information (2017, methodology): “, 2011; White, 1982), in the reconciliation of 17 frequentist and Bayesian estimation methods through the Bernstein-von Mises theorem (Bickel 18 and Kleijn, 2012; Rivoirard and Rousseau, 2012; van der Vaart, 1998; Yang and Le Cam, 2000), 19 in statistical decision theory (e.g., Berger, 1985; Hájek, ”