A characterization of limiting distributions of regular estimates

By J. Hájek. 1970

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Citations in the corpus

Geometric Lower Bounds for Distributed Parameter Estimation Under Communication Constraints (2018, background): “Corollary 5 completely characterizes the minimax risk for distribution estimation under general (n, k, d) Han et al. (2018), which improves over Diakonikolas et al.”
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,…”
A Tutorial on Fisher Information (2017, background): “For details see the advanced accounts provided by Bickel et al. (1993), Hájek (1970), Inagaki (1970) and LeCam (1970).”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, background): “[13] L. Le Cam, Asymptotic methods in statistical decision theory.”
Applications of the van Trees inequality : a Bayesian Cramr-Rao bound (1995, background): “(More general version of this elementary result is known as the Hájek’s convolution theorem; see Hájek (1970).”
ON DIFFERENTIABLE FUNCTIONALS (1988, background): “This follows (almost) directly from Hajek (1972) and the fact that (3.”
Efficiently Breaking the Curse of Horizon: Double Reinforcement Learning in Infinite-Horizon Processes (2019, methodology): “In the iid setting, we can let R N = R , the CR bound is independent of n , and 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…”
Bias-Reduced Doubly Robust Estimation (2015, methodology): “6 projection (Hájek 1970; van der Vaart 1998) of ν̂n,0, which is given by”
ON THE ASYMPTOTIC EFFICIENCY OF GMM (2013, background): “By the convolution theorem (Hajek, 1970), we have L = M ∗ N where M is independent of N and N is a normal with mean zero and variance E ( ss′ )−1.”
Statistically Efficient Off-Policy Policy Gradients (2020, unknown): “In parametric models, the Cram´er-Rao bound lower bounds the variance of all unbiased estimators and, due to H´ajek (1970), also the asymptotic MSE of all (regular) estimators.”
The semiparametric Bernstein-von Mises theorem (2010, background): “Hájek’s convolution theorem (Hájek [17]) implies that within the class of regular estimates, asymptotic variance is lower-bounded by the Cramér–Rao bound in the limit experiment [29].”
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].”