Information and the Accuracy Attainable in the Estimation of Statistical Parameters

By Calyampudi R. Rao. 1992

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Citations in the corpus

A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms (2019, methodology): “In addition to the gradient estimate provided by Proposition 6, we can also derive a Rao-Blackwellized (Rao, 1992; Blackwell, 1947) estimate of the gradient of the regret, based on the formulation derived in Proposition 5.”
Cramer-Rao Lower Bound and Information Geometry (2013, methodology): “Statistical distances play a key role in tests of significance and classification [43].”
Fisher Information Under Local Differential Privacy (2020, methodology): “Under some mild regularity conditions, the Fisher information at a point θ in the space of possible parameters immediately gives a lower bound on the squared 2 risk for estimating θ via the well-known Cramér-Rao bound for unbiased estimators [5], [6], [7, Sec.”
Lightlike Neuromanifolds, Occam's Razor and Deep Learning (2019, background): “…geometry [16] studies such a space in the Riemannian and more generally differential geometry framework Hotelling [15] (1930) and independently Rao [36, 37] (1945) proposed to endow a parametric space of statistical models with the Fisher information matrix as a Riemannian metric where E p denotes…”
A Survey on Fundamental Limits of Integrated Sensing and Communication (2021, background): “To gain more insights on the performance limits, a few lower bounds on MSEθ have been proposed in the literature [58], [57] and [59].”
Location–Scale Depth (2004, background): “It may be of some interest that the hyperbolic geometry of the Student depth coincides with the Riemannian geometry generated by the Fisher information matrix, the so-called information geometry introduced by Rao (1945) and Jeffreys (1946); see Kass and Voss (1997).”
QUANTILE ESTIMATION WITH ADAPTIVE IMPORTANCE SAMPLING (2010, methodology): “The usage of the Riemannian metric based on the Fisher information goes back to [28].”
Pursuit and an evolutionary game (2009, methodology): “The former is well known and attributed to Rao (1945), based on Fisher’s information matrix (Fisher 1922), while the latter (first referred to as the Shahshahani metric by Akin (1979)) was ‘invented’ by Shahshahani (1979), apparently without prior knowledge of the work of Fisher and Rao.”
Riemann manifold Langevin and Hamiltonian Monte Carlo methods (2011, methodology): “Experimental results for Log-Gaussian Cox processes Following the example given by Christensen et al. (2005), we fix the parameters β = 1=33, σ2 = 1:91 and μ = log.126/ − σ2=2. We generate a latent Gaussian field x from the Gaussian process and use these values to generate count data y from the late”
Natural Gradient Works Efficiently in Learning (1998, methodology): “The Riemannian structure of the parameter space of a statistical model is defined by the Fisher information (Rao, 1945; Amari, 1985)”
Diffusion Kernels on Statistical Manifolds (2005, background): “This geometry has long been recognized (Rao, 1945), and there is a rich line of research in statistics, with threads in machine learning, that has sought to exploit this geometry in statistical analysis; see Kass (1989) for a survey and discussion, or the monographs by Kass and Vos (1997) and Amari ”
A Theory of Cramer-Rao Bounds for Constrained Parametric Models (2010, methodology): “(3.40) In this formulation, the well-known Rao and Wald statistics were shown in section 2.5.”