Goodness-of-fit test statistics that dominate the Kolmogorov statistics

  • Robert H. Berk
  • Douglas H. Jones
Article

DOI: 10.1007/BF00533250

Cite this article as:
Berk, R.H. & Jones, D.H. Z. Wahrscheinlichkeitstheorie verw Gebiete (1979) 47: 47. doi:10.1007/BF00533250

Summary

Two statistics are proposed for the simple goodness-of-fit problem. These are derived from a general principle for combining dependent test statistics that has been discussed elsewhere by the authors. It is shown that these statistics are relatively optimal in the sense of Bahadur efficiency and consequently, are more efficient than any weighted Kolmogorov statistic at every alternative. A curious pathology occurs: Under certain alternatives, the sequence of statistics has a Bahadur efficacy or exact slope only in the weak sense of convergence in law.

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Robert H. Berk
    • 1
  • Douglas H. Jones
    • 1
  1. 1.Department of StatisticsRutgers UniversityNew BrunswichUSA

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