Distribution of the Anderson-Darling Statistic

General Saddlepoint Approximations: Application to the Anderson-Darling Test Statistic

We consider the relative merits of various saddlepoint approximations for the c.d.f. of a statistic with a possibly non-normal limit distribution. In addition to the usual Lugannani-Rice approximation we also consider approximations based on higher-order expansions, including the case where the base distribution for the approximation is taken to be non-normal. This extends earlier work by Wood ...

A Saddlepoint Approximation to the Distribution Function of the Anderson-Darling Test Statistic

The Anderson-Darling goodness-of-fit test has a highly skewed and non-standard limit distribution. Various attempts have been made to tabulate the associated critical points, using both theoretical approximations and simulation methods. We show that a standard saddlepoint approximation performs well in both tails of the distribution. It is markedly superior to other theoretical approximations i...

K-Sample Anderson-Darling Tests

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Anderson-Darling Tests of Goodness-of-Fit

Random Projection-Based Anderson-Darling Test for Random Fields

In this paper, we present the Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) goodness of fit statistics for stationary and non-stationary random fields. Namely, we adopt an easy-to-apply method based on a random projection of a Hilbert-valued random field onto the real line R, and then, applying the well-known AD and KS goodness of fit tests. We conclude this paper by studying the behavior o...