Reweighted and Circularized Anderson-Darling Tests of Goodness-of-Fit

TL;DR

This paper introduces circularized Anderson-Darling tests, which improve goodness-of-fit testing by leveraging geometric insights and circular symmetry, demonstrating superior finite-sample performance and establishing new large-sample theoretical results.

Contribution

It proposes circularized tests based on reweighted Anderson-Darling statistics, offering a novel approach with better performance and theoretical foundations.

Findings

Circularized tests outperform parent methods in simulations.

The tests have good finite-sample performance.

New large-sample theoretical results are established.

Abstract

This paper takes a look at omnibus tests of goodness of fit in the context of reweighted Anderson-Darling tests and makes threefold contributions. The first contribution is to provide a geometric understanding. It is argued that the test statistic with minimum variance for exchangeable distributional deviations can serve as a good general-purpose test. The second contribution is to propose better omnibus tests, called circularly symmetric tests and obtained by circularizing reweighted Anderson-Darling test statistics or, more generally, test statistics based on the observed order statistics. The resulting tests are called circularized tests. A limited but arguably convincing simulation study on finite-sample performance demonstrates that circularized tests have good performance, as they typically outperform their parent methods in the simulation study. The third contribution is to establish new large-sample results.