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Data-driven stabilizations of goodness-of-fit tests

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  • Fernández de Marcos Giménez de los Galanes, Alberto
  • García Portugués, Eduardo

Abstract

Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the form of a lookup table or carried out on demand, to apply a goodness-of-fit test. Stephens (1970) provided remarkable simple and useful transformations of several classic goodness-of-fit test statistics that stabilized their exact-n critical values for varying sample sizes n. However, detail on the accuracy of these and subsequent transformations in yielding exact p-values, or even deep understanding on the derivation of several transformations, is still scarce nowadays. We illuminate and automatize, using modern tools, the latter stabilization approach to (i) expand its scope of applicability and (ii) yield semi-continuous exact p-values, as opposed to exact critical values for fixed significance levels. We show improvements on the stabilization accuracy of the exact null distributions of the Kolmogorov-Smirnov, Cramér-von Mises, Anderson-Darling, Kuiper, and Watson test statistics. In addition, we provide a parameter-dependent exact-n stabilization for several novel statistics for testing uniformity on the hypersphere of arbitrary dimension. A data application in astronomy illustrates the benefits of the advocated stabilization for quickly analyzing small-to-moderate sequentially-measured samples.

Suggested Citation

  • Fernández de Marcos Giménez de los Galanes, Alberto & García Portugués, Eduardo, 2022. "Data-driven stabilizations of goodness-of-fit tests," DES - Working Papers. Statistics and Econometrics. WS 35324, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:35324
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    References listed on IDEAS

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