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Improving the Bickel–Rosenblatt global measure of deviation and goodness-of-fit test

Author

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  • Ahmed, S. Ejaz
  • Amezziane, Mohamed
  • Dahal, Keshab

Abstract

We propose a zero-centered version of the Bickel–Rosenblatt statistic and use it to construct goodness of fit tests. We derive the null distributions and power functions of these tests along with their consistency results. A simulation study is carried out to show how the new tests outperform traditional ones.

Suggested Citation

  • Ahmed, S. Ejaz & Amezziane, Mohamed & Dahal, Keshab, 2025. "Improving the Bickel–Rosenblatt global measure of deviation and goodness-of-fit test," Statistics & Probability Letters, Elsevier, vol. 218(C).
    • Handle: RePEc:eee:stapro:v:218:y:2025:i:c:s0167715224002797
    DOI: 10.1016/j.spl.2024.110310
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    References listed on IDEAS

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    1. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
    2. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 437-453.
    3. Pavia, Jose M., 2015. "Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(c01).
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