On the composition of elementary errors

By Anders Martin-Löf. 1994

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Citations in the corpus

Alternatives to the Chi-Square Test for Evaluating Rank Histograms from Ensemble Forecasts (2005, methodology): “These tests are based on the Cramér–von Mises, Watson, and Anderson–Darling statistics.”
Energy statistics: A class of statistics based on distances (2013, background): “was introduced in Cramér (1928). This distance has the disadvantage that it is not distribution-free; thus if we want to apply this distance for testing goodness-of-fit, then the critical values depend on F.”
Causality detection based on information-theoretic approaches in time series analysis (2007, background): “Edgeworth expansion is consistent, i.e. in inﬁnity converges to the function which it expands, Cramer [52].”
Multivariate goodness-of-fit tests based on Wasserstein distance (2020, background): “The most popular ones are the Cramér–von Mises (Cramér, 1928; von Mises, 1928) and Kolmogorov–Smirnov (Kolmogorov, 1933; Smirnov, 1939) tests, involving distances between the cumulative distribution function of P0 and the empirical one.”
Powerful goodness‐of‐fit tests based on the likelihood ratio (2002, unknown): “2.3. dw(t) = F0(t) {1 – F0(t)} dF0(t) Replacing Zt of the first of equations (1.1) with X2t generates the famous Cramér–von Mises statistic (Cramér, 1928; von Mises, 1931; Smirnov, 1936, 1937; Stephens, 1970, 1974; Knott, 1974; D’Agostino and Stephens, 1986; Csörgő and Faraway, 1996; Spinelli and…”
Hypothesis Testing For Densities and High-Dimensional Multinomials: Sharp Local Minimax Rates (2017, methodology): “Testing Lipschitz densities is one of the basic non-parametric hypothesis testing problems and tests are often based on the Kolmogorov-Smirnov or Cramér-von Mises statistics [7, 27, 31].”
Detecting Out-of-Distribution Inputs to Deep Generative Models Using a Test for Typicality (2019, background): “Many of the classical GoF tests rely on access to the cumulative distribution function (CDF) of interest and/or being able to compute an empirical distribution function (EDF) [12, 25, 2, 35].”
Extropy estimators with applications in testing uniformity (2018, methodology): “Those statistics are given as follows including Kolmogrov–Smirnov statistic (Kolmogorov 1933; Smirnov 1939), Anerson–Darling statistic (Anderson and Darling 1954), Cramer–vonMises statistic (Cramér 1928; vonMises 1931) and Zamanzade statistic (Zamanzade 2015).”
Powers of Discrete Goodness-of-Fit Test Statistics for a Uniform Null Against a Selection of Alternative Distributions (2006, methodology): “The test statistics specified in Table 1 are discrete versions of goodness-of-fit test statistics for continuous distributions developed by Kolmogorov (1933), Smirnov (1939), Cramér (1928), and Anderson and Darling (1952).”
Variations of Q–Q Plots: The Power of Our Eyes! (2015, methodology): “…for the test statistics of the Kolmogorov-Smirnov (KS-test, Kolmogorov, 1933; Smirnov, 1948), the Lilliefors (LF-test, Lilliefors, 1967), the AndersonDarling (AD-test, Anderson and Darling, 1954), and the Cramér-von-Mises tests (CVM-test, Cramér, 1928; von Mises, 1928), as shown in table 1.”
Data-Driven Methods for Adaptive Spoken Dialogue Systems (2012, methodology): “[8] train SLU models on the ATIS, MEDIA, and LUNA corpora.”
On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests (2015, methodology): “The KS test, the related Cramer von-Mises criterion by [22,23], and Anderson–Darling test by [24] are very popular in one dimension, but their usage has been more restricted in higher dimensions.”
Restricted isometry properties and nonconvex compressive sensing (2007, background): “Since this is the sum of M independent random variables, what is needed can be thought of as a quantitative, nonasymptotic form of the central limit theorem.”
Computation of Probability Associated with Anderson–Darling Statistic (2018, unknown): “The most frequently used goodness-of-fit tests are Kolmogorov–Smirnov [3,4], Anderson–Darling [5,6], Pearson’s chi-square [7], Cramér–von Mises [8,9], Shapiro–Wilk [10], Jarque–Bera [11–13], D’Agostino–Pearson [14], and Lilliefors [15,16].”