Applications of the van Trees inequality : a Bayesian Cramr-Rao bound

By R. Gill, B. Levit. 1995

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Citations in the corpus

Learning Distributions from their Samples under Communication Constraints (2019, methodology): “We could have equivalently used the multivariate version of the van Trees inequality [16] to arrive at the same result, but we have used the single-variable version in each coordinate instead in order to simplify the required regularity conditions.”
On recursive estimation for time varying autoregressive processes (2005, background): “ ﬁrst inequality is the Bayesian lower bound of the minimax risk [recall that, for nsuﬃciently large, (ηφn,t,σ)∈C for all |η|≤v−1 n ], the second inequality is the so-called van Trees inequality (see [11]) with In(η) denoting the Fisher information of the translation model associated with the p.d.f.”
Fisher Information Under Local Differential Privacy (2020, methodology): “…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 biased estimators) [11].”
Dynamic Pricing with an Unknown Demand Model: Asymptotically Optimal Semi-Myopic Policies (2014, methodology): “Invoking the multivariate van Trees inequality (Gill and Levit 1995), we obtain”
Quantum-enhanced measurements without entanglement (2017, methodology): “This includes the van Trees inequality (Gill and Levit, 1995; van Trees, 2001), Bayesian approaches (Macieszczak et al., 2014; Rivas and Luis, 2012), adaptive measurements (Armen et al., 2002; Berry and Wiseman, 2000, 2002, 2006, 2013; Fujiwara, 2006; Higgins et al., 2009; Okamoto et al., 2012;…”
Deconvolution of supersmooth densities with smooth noise (2004, methodology): “We apply at this point the van Trees inequality (see Gill & Levit 1995) for the Bayesian risk in the deconvolution model and get where I(8) is the Fisher information of (fe * f ) ~ E [ - ~ , , , ~ , , ] = (fr)eE[-,g,,e,l in the deconvolution model.”
A Geometric Characterization of Fisher Information from Quantized Samples with Applications to Distributed Statistical Estimation (2018, methodology): “In order to lower bound this risk, we will use the van Trees inequality from [17].”
Lower Bounds for Learning Distributions under Communication Constraints via Fisher Information (2019, methodology): “In order to lower bound this risk, we will use the van Trees inequality [29].”
Minimax Bounds for Distributed Logistic Regression (2019, unknown): “The van Trees inequality is a Bayesian version of the Cramér-Rao lower bound, which in the version we will use from Gill and Levit (1995), bounds the average ℓ2 risk by ∫ Θ Eθ‖θ̂ − θ‖ 2 2µ(θ)dθ ≥ d2 Tr(IM1,...,Mn(θ)) + J(µ) (1) where µ(θ) = ∏d j=1 µj(θj) is a prior for the parameter θ,…”
Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, background): “[73] Under assumptions above, the average risk of an arbitrary estimator ψ̂(X) in estimating an absolutely continuous functional ψ(θ) under squared error loss satisfies the following inequality:”
On Bayes Risk Lower Bounds (2014, background): “, where H ( P || Q ) = ( p − q ) 2 1 / 2 is the Hellinger distance between P and Q .”
Minimax Estimation of Functionals of Discrete Distributions (2014, background): “However, these follow respectively from the standard information bound such as [15], and the well-known asymptotic efficiency of the MLE [16].”
Subdiffraction incoherent optical imaging via spatial-mode demultiplexing (2016, background): “This issue depends on the parameterization [44] and does not arise for the moment parameters, however.”
A Linear Response Bandit Problem (2013, unknown): “In particular, by the van Trees inequality [see Gill and Levit (1995)] (37) inf δt−1 ∫ E|δt−1 − θ|(2)l(θ)dθ ≥ 1 It−1 + I(l) , where It−1 is the expected Fisher information for θ associated with the conditional density of the observations Yt−1 given θ; and I(l) is the Fisher information for the locat”