Asymptotic Behavior of Cox's Partial Likelihood and its Application to Variable Selection
Autor: | Ye Yu, Jian Jian Ren, Guangren Yang, Runze Li |
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Rok vydání: | 2017 |
Předmět: |
Statistics and Probability
Logarithm Model selection 05 social sciences Expected value 01 natural sciences Article Statistics::Computation 010104 statistics & probability Bayesian information criterion Sample size determination 0502 economics and business Statistics Linear regression Statistics::Methodology 0101 mathematics Statistics Probability and Uncertainty Akaike information criterion Selection (genetic algorithm) 050205 econometrics Mathematics |
Zdroj: | Statistica Sinica. |
ISSN: | 1017-0405 |
Popis: | 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 C(p), 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. |
Databáze: | OpenAIRE |
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