Mathematical methods of statistics

By H. Cramér. 1946

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Citations in the corpus

Detecting non-causal artifacts in multivariate linear regression models (2018, background): “[2006], Hoyer et al. [2009], Zhang and Hyvärinen [2009], Blöbaum et al.”
Counterfactual reasoning and learning systems: the example of computational advertising (2012, neutral): “Since the samples `(ωi) w̄(ωi) are independent and identically distributed, the central limit theorem (e.g., Cramér, 1946, section 17.4) states that the empirical average Ŷ ∗ converges in law to a normal distribution of mean Ȳ ∗ = E[`(ω) w̄(ω)] and variance V̄ = var[`(ω) w̄(ω)].”
Causal Inference Using the Algorithmic Markov Condition (2008, methodology): “To this end, we introduce a concept from statistical estimation theory [44].”
On asymptotically optimal confidence regions and tests for high-dimensional models (2013, methodology): “1 means that we regress to the classical conditions for asymptotic normality in the onedimensional case as in, for example, [15].”
Some Parameter Estimation Issues in Functional-Structural Plant Modelling (2011, methodology): “3) In this article, we choose to use the maximum likelihood estimator since it often has some optimal properties, like asymptotic efficiency (see for example [11]).”
Probabilistic Power Flow Studies for Transmission Systems With Photovoltaic Generation Using Cumulants (2012, methodology): “Reference [19] shows that under fairly general conditions, the Edgeworth expansion has asymptotic properties, which means that the difference between the true function and the partial series of the first terms is of a lower order than the term in the sum [20].”
Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry (2013, background): “The roots of these connections go back much further—to Cramér (1946) (the idea of the concentration ellipsoid), to Pearson (1901) and Hotelling (1933) (principal components), and, we maintain, ultimately to Galton (1886).”
Geometrical Insights for Implicit Generative Modeling (2017, background): “This criterion is particularly convenient because it enjoys favorable statistical properties [14] and because its optimization can be written as an expectation with respect to the data distribution,”
Building Better Open-Source Tools to Support Fairness in Automated Scoring (2017, methodology): “To explore the impact of such factors, RSMTool computes two types of correlations: (a) the marginal correlation between each feature and the covariate, and (b) the “partial” correlation be-tween each feature and the human score, with the effects of the covariate removed (Cram´er, 1947).”
Bayes factors based on test statistics (2005, unknown): “θ/ > c 2 > 0 for all i, and let θ̂ denote the maximum likelihood estimate of θ (or another efficient estimator of θ in the sense that was specified in Cramér (1946)).”
Iterative maximum-likelihood reconstruction in quantum homodyne tomography (2003, methodology): “A typical way of estimating uncertainties in MaxLik algorithms is by diagonalizing the Fisher information matrix [21, 22].”
A deep learning approach for detecting traffic accidents from social media data (2018, methodology): “The benchmark we choose for individual token features is phi coefficient (Cramér, 1999), which can measure the association between manual label and tokens.”
Extending the Search for Muon Neutrinos Coincident with Gamma-Ray Bursts in IceCube Data (2017, methodology): “For use in the significance calculation in this analysis, the reconstructed angular uncertainty is determined using the Cramer–Rao lower bound (Cramer 1945; Rao 1945) on the covariance of angular direction measures from the inverse of the likelihood Fisher information matrix. Finally, the muon energ”
Jammed hard-particle packings: From Kepler to Bernal and beyond (2010, methodology): “Two continuous probability densities that have been widely used to characterize physical phenomena are the Schulz (Schulz, 1939) and log-normal (Cramer, 1954) distributions.”