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Cumulants and Bartlett Identities in Cox Regression

In: The Fascination of Probability, Statistics and their Applications

Author

Listed:
  • Per Aslak Mykland

    (The University of Chicago, Department of Statistics)

  • Jianming Ye

    (Baruch College, Zicklin School of Business
    Xiamen University, School of Management)

Abstract

Expressions are found for the cumulants needed to analyze and improve the accuracy of Cox regression up to order $$O(n^{-3/2})$$ O ( n - 3 / 2 ) , and consistent estimators for these are given. In addition, the Bartlett identities are shown to hold for the Cox partial likelihood (and, in a broad sense, for partial likelihood in general), so that the cumulant estimators found can be used to adjust statistics in accordance with formulas from likelihood theory. Numerical results are also given.

Suggested Citation

  • Per Aslak Mykland & Jianming Ye, 2016. "Cumulants and Bartlett Identities in Cox Regression," Springer Books, in: Mark Podolskij & Robert Stelzer & Steen Thorbjørnsen & Almut E. D. Veraart (ed.), The Fascination of Probability, Statistics and their Applications, pages 85-97, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-25826-3_5
    DOI: 10.1007/978-3-319-25826-3_5
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