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Title of Journal: Ann Inst Stat Math

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Abbravation: Annals of the Institute of Statistical Mathematics

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Springer-Verlag

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10.1007/978-3-319-20294-5_58

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1572-9052

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Full likelihood inferences in the Cox model an em

Authors: JianJian Ren Mai Zhou
Publish Date: 2010/02/18
Volume: 63, Issue: 5, Pages: 1005-1018
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Abstract

For the regression parameter β 0 in the Cox model there have been several estimators constructed based on various types of approximated likelihood but none of them has demonstrated smallsample advantage over Cox’s partial likelihood estimator In this article we derive the full likelihood function for β 0 F 0 where F 0 is the baseline distribution in the Cox model Using the empirical likelihood parameterization we explicitly profile out nuisance parameter F 0 to obtain the fullprofile likelihood function for β 0 and the maximum likelihood estimator MLE for β 0 F 0 The relation between the MLE and Cox’s partial likelihood estimator for β 0 is made clear by showing that Taylor’s expansion gives Cox’s partial likelihood estimating function as the leading term of the fullprofile likelihood estimating function We show that the log fulllikelihood ratio has an asymptotic chisquared distribution while the simulation studies indicate that for small or moderate sample sizes the MLE performs favorably over Cox’s partial likelihood estimator In a real dataset example our full likelihood ratio test and Cox’s partial likelihood ratio test lead to statistically different conclusions

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  1. Estimating nonlinear regression with and without change-points by the LAD method
  2. Smoothing algorithms for state–space models
  3. Maximum likelihood estimation in the proportional hazards cure model
  4. Conditional independence, conditional mixing and conditional association
  5. Two-step estimation procedures for inhomogeneous shot-noise Cox processes
  6. Estimating the intensity of a cyclic Poisson process in the presence of linear trend
  7. Recursive equations in finite Markov chain imbedding
  8. Connectedness of PBIB designs having asymmetrical association schemes
  9. Limiting size index distributions for ball-bin models with Zipf-type frequencies
  10. Higher-order accurate polyspectral estimation with flat-top lag-windows
  11. A class of rank-based test for left-truncated and right-censored data
  12. Local c - and E -optimal Designs for Exponential Regression Models
  13. A characterization of limiting distributions of estimators in an autoregressive process
  14. Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise
  15. Yates type estimators of a common mean
  16. On sum of 0–1 random variables I. Univariate case
  17. Nonparametric estimators of the survival function with twice censored data
  18. Testing Homogeneity in Weibull Error in Variables Models
  19. Goodness of fit test for ergodic diffusion processes
  20. Proportional odds frailty model and stochastic comparisons
  21. Multiplicity distributions in a two-component branching process
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