Theory of statistical inference and information

By Igor Vajda. 1989

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Citations in the corpus

On the empirical estimation of integral probability metrics (2012, neutral): “2) is known for (S, ρ(x, y)) = (R, |x− y|) [47, 48], and given as W1(P,Q) = ∫”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, methodology): “Popular examples for γ in these statistical applications include the Kullback-Leibler divergence, the total variation distance, the Hellinger distance (Vajda, 1989) — these three are specific instances of the generalized φ-divergence (Ali and Silvey, 1966; Csiszár, 1967) — the Kolmogorov distance…”
On integral probability metrics, φ-divergences and binary classification (2009, background): “6The explicit form for the Wasserstein distance in (3) is knowfor (M, ρ(x, y)) = (R, |x − y|) [16], [38], which is given asW1(P, Q) = ∫”
On Semiparametric estimation in Single-Index Regression (2006, unknown): “Another example is provided by the so-called α−estimator defined by ρ (t) = 1− e−αt2 (cf. Vajda (1989)).”
Medical image registration using mutual information (2003, methodology): “Some properties of mutual information are summarized in Table 1 (see [114] for their proof).”
Distributionally Robust Optimization: A Review (2019, methodology): “For detailed information on φ-divergences, we refer to Read and Cressie [254], Vajda [306], Pardo [226].”
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities (2010, methodology): “For example, using the Amari notation, αA with α = (1− αA)/2, the Alpha-divergence takes the following form [1–3,10,11,22–25,44,48,49]:”
REGO: Rank-based Estimation of Renyi Information using Euclidean Graph Optimization (2010, background): “Further, F j being a measurable invertible mapping, I (cid:11) ( Z ) = I (cid:11) ( X ), by the isomorphism theorem (Vajda, 1989).”
Robust estimation for non-homogeneous data and the selection of the optimal tuning parameter: the density power divergence approach (2015, background): “See Vajda [13], Pardo [10] and Basu et al. [2] for an elaborate description of the theory of minimum distance inference and several illustrative examples.”
On Pinsker's and Vajda's Type Inequalities for Csiszár's $f$ -Divergences (2006, background): “Second, Vajda showed in [37] that the lower bound is convex, increasing and, for many 's, satisfies that as (see also [38]).”
Rényi divergence measures for commonly used univariate continuous distributions (2013, background): “−π ln h(λ) φ(λ)1−αψ(λ)α dλ [31] h(λ) := αψ(λ) + (1− α)φ(λ)”
On the measure of the information in a statistical experiment (2007, background): “These numbers, known as Csiszár divergences, were independently related to the information in E by Csiszár (1963, 1967) and by Ali and Silvey (1966), and their statistical meaning stems from their relation to the Bayes risk when testing θj against θi (see, e.g., Torgersen 1991b, 1994; Vajda 1989).”
Mutual-information-based registration of medical images: a survey (2003, background): “Most books on information theory ([16]–[18], for example) discuss the notion of mutual information.”