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

TY - JOUR

T1 - Goodness-of-fit test statistics that dominate the Kolmogorov statistics

AU - Berk, Robert H.

AU - Jones, Douglas H.

PY - 1979/1

Y1 - 1979/1

N2 - 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.

AB - 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.

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U2 - 10.1007/BF00533250

DO - 10.1007/BF00533250

M3 - Article

SN - 0044-3719

VL - 47

SP - 47

EP - 59

JO - Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete

JF - Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete

IS - 1

ER -