Cumulants and Bartlett Identities in Cox Regression by Per

Expressions are found for the cumulants needed to analyze Cox regression up to order 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. 1 Per A. Mykland is Assistant Professor, Department of Statistics, University of Chicago, Chicago, IL 60637. Research was supported in part by National Science Foundation grant DMS 93-05601. 2 Jianming Ye is Assistant Professor, Graduate School of Business, University of Chicago, Chicago, IL 60637. Research was supported in part by The University of Chicago Graduate School of Business Research Fund. This manuscript was prepared using computer facilities supported in part by the National Science Foundation grants DMS 89-05292, DMS 87-03942, and DMS 86-01732 awarded to the Department of Statistics at The University of Chicago, and by The University of Chicago Block Fund.