Geometrical foundations of asymptotic inference

By Ted Chang. 2002

237 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, History and Philosophy of Science

View Paper: https://www.semanticscholar.org/paper/cf6c29331cab192af98553f453ce253a408d9381

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In Computational Theory and Mathematics

In History and Philosophy of Science

Citations in the corpus

Perturbation selection and influence measures in local influence analysis (2007, background): “The geodesic is a direct extension of the straight line ω(t) = ω0 + th in Euclidean space (Amari [1] and Kass and Vos [14]).”
Identification and Likelihood Inference for Recursive Linear Models with Correlated Errors (2006, unknown): “Similarly, model selection criteria, such as BIC [47], are called into question as consistency results have been proved only for curved exponential families [22] [26] [28].”
Philosophy and the practice of Bayesian statistics (2010, unknown): “…likelihood.7 There is a geometric sense in which these parts of the parameter space are closest approaches to the truth within the support of the prior (Kass and Vos, 1997), but they may or may not be close to the truth in the sense of giving accurate values for parameters of scientific interest.”
Algebraic statistical models (2007, background): “An exponential family induced by a smooth manifold in the natural parameter space is commonly termed a curved exponential family ; see Kass and Vos (1997) for an introduction to this topic.”
Information geometry on hierarchy of probability distributions (2001, background): “The present paper studies such a hierarchical structure and the related invariant " quasi-orthogonal " quantitative decomposition by using information geometry [3], [8], [12], [14], [28], [30].”
A tutorial introduction to the minimum description length principle (2004, background): “(2.25) Here Î(xn) is the so-called observed information, sometimes also called observed Fisher information; see [Kass and Voss 1997] for a definition.”
Cramer-Rao Lower Bound and Information Geometry (2013, background): “Since the seminal work of Rao [6] in 1945, the interplay of differential geometry with statistics has further strengthened and developed into a new discipline called information geometry with a few dedicated monographs [5, 40, 30, 6, 46, 7].”
Information geometry and sufficient statistics (2012, unknown): “We refer the reader to [33], [25] and [4] for more extensive historical remarks and guide on other important contributions in the ﬁeld.”
The epic story of maximum likelihood (2007, unknown): “It was an investigation of the differential geometry of parameter spaces, with what is sometimes called the Jeffreys information metric, after Jeffreys (1946) (Kass, 1989; Kass and Vos, 1997).”
Information-Geometric Dimensionality Reduction (2011, methodology): “As a pair of densities approach e other, the Kullback-Leibler divergence is a good approximation to the Fisher information distance b etween them2 [14]:”
Discrete chain graph models (2009, background): “, they are curved exponential families [17]).”
Self-Consuming Generative Models Go MAD (2023, methodology): “• Generative adversarial network: We use an unconditional StyleGAN2 architecture [58] trained on the FFHQ-128×128 dataset [63].”
Likelihood ratio tests and singularities (2007, background): “exponential family and Θ0 a smooth manifold, in which case the submodel PΘ0 = (Pθ | θ ∈Θ0) is called a curved exponential family [18].”
Diffusion Kernels on Statistical Manifolds (2005, background): “…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 and Nagaoka (2000) for more extensive treatments.”
Differential Geometry of Special Mappings (2019, background): “The results of these researches are reflected in the following monographs [5, 6, 84, 111, 130] etc.”