Asymptotic behavior of Cox's partial likelihood and its application to variable selection

Runze Li, Jian Jian Ren, Guangren Yang, Ye Yu

Research output: Contribution to journalArticle

Abstract

For theoretical properties of variable selection procedures for Cox's model, we study the asymptotic behavior of partial likelihood for the Cox model. We find that the partial likelihood does not behave like an ordinary likelihood, whose sample average typically tends to its expected value, a finite number, in probability. Under some mild conditions, we prove that the sample average of partial likelihood tends to infinity at the rate of the logarithm of the sample size, in probability. We apply the asymptotic results on the partial likelihood to study tuning parameter selection for penalized partial likelihood. We find that the penalized partial likelihood with the generalized cross-validation (GCV) tuning parameter proposed in Fan and Li (2002) enjoys the model selection consistency property, despite the fact that GCV, AIC and Cp, equivalent in the context of linear regression models, are not model selection consistent. Our empirical studies via Monte Carlo simulation and a data example confirm our theoretical findings.

Original languageEnglish (US)
Pages (from-to)2713-2731
Number of pages19
JournalStatistica Sinica
Volume28
Issue number4
DOIs
StatePublished - Oct 1 2018

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Partial Likelihood
Variable Selection
Asymptotic Behavior
Generalized Cross-validation
Penalized Likelihood
Cox Model
Model Selection
Tend
Parameter Selection
Selection Procedures
Parameter Tuning
Linear Regression Model
Expected Value
Logarithm
Empirical Study
Variable selection
Asymptotic behavior
Tuning
Likelihood
Sample Size

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Li, Runze ; Ren, Jian Jian ; Yang, Guangren ; Yu, Ye. / Asymptotic behavior of Cox's partial likelihood and its application to variable selection. In: Statistica Sinica. 2018 ; Vol. 28, No. 4. pp. 2713-2731.
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Asymptotic behavior of Cox's partial likelihood and its application to variable selection. / Li, Runze; Ren, Jian Jian; Yang, Guangren; Yu, Ye.

In: Statistica Sinica, Vol. 28, No. 4, 01.10.2018, p. 2713-2731.

Research output: Contribution to journalArticle

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