Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes

By Theodore W. Anderson, D. Darling. 1952

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Citations in the corpus

TestU01: A C library for empirical testing of random number generators (2006, background): “Their (approximate) distributions under H0 can be found in Anderson and Darling [1952], Darling [1960], Durbin [1973], Stephens [1970], Stephens [1986a], and Sinclair and Spurr [1988]. The p-value of the GOF test statistic is computed and H0 is rejected if this p-value is deemed too extreme, as usua”
An empirical power comparison of univariate goodness-of-fit tests for normality (2010, background): “The Anderson-Darling test Anderson and Darling [39] proposed a test statistic AD of the form AD = n ∫ ∞ −∞ [Fn(x) − (x)]2ψ(x)dF(x) where Fn(x) is the empirical distribution function (EDF), (x) is the cumulative distribution function of the standard normal distribution and ψ(x) is a weight function g”
Alternatives to the Chi-Square Test for Evaluating Rank Histograms from Ensemble Forecasts (2005, methodology): “This family consists of the Cramér– von Mises (Cramér 1928; von Mises 1931; Smirnov 1936), the Watson (Watson 1961), and the Anderson– Darling (Anderson and Darling 1952) tests.”
Composite Goodness-of-Fit Tests for Left-Truncated Loss Samples (2015, background): “1 Related works on the discussion of these widely used tests include Anderson and Darling (1952), Anderson and Darling (1954), D’Agostino and Stephens (1986), Schorack and Wellner (1986).”
Dealing with Structural Breaks (2005, methodology): “He showed that Q ⇒ Z 1 0 B 0 (r) 2 dr where B 0 (r) = W (r) − rW (1) is a Brownian bridge, and noted that percentage point had already been derived by Anderson and Darling (1952) in the context of goodness of fit tests.”
Deriving robust counterparts of nonlinear uncertain inequalities (2014, unknown): “Instead of using φ-divergence test statistics, one could also use the well-known AndersonDarling test statistic [2] for the definition of the uncertainty region.”
Comparing distributions by multiple testing across quantiles or CDF values (2017, background): “Anderson and Darling (1952) gave exactly this solution in their Example 2 (p.”
Evaluating the Anderson-Darling Distribution (2004, background): “Anderson and Darling [2] used numerical integration to find the 90, 95 and 99 percentiles.”
Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications (2006, unknown): “A test statistic which is superior in this regard dates back to Anderson and Darling (1952).”
New tests of the correspondence between unitary eigenvalues and the zeros of Riemann's zeta function (2000, methodology): “The first test is the Anderson–Darling test [1].”
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].”