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Inference with penalized likelihood

This work studies the statistical properties of the maximum penalized likelihood approach in a semi-parametric framework. We recall the penalized likelihood approach for estimating a function and review some asymptotic results. We investigate the properties of two estimators of the variance of maximum penalized likelihood estimators: sandwich estimator and a Bayesian estimator. The coverage rates of confidence intervals based on these estimators are studied through a simulation study of survival data. In a first simulation the coverage rates for the survival function and the hazard function are evaluated. In a second simulation data are generated from a proportional hazard model with covariates. The estimators of the variances of the regression coefficients are studied. As for the survival and hazard functions, both sandwich and Bayesian estimators exhibit relatively good properties, but the Bayesian estimator seems to be more accurate. As for the regression coefficients, we focussed on the Bayesian estimator and found that it yielded good coverage rates.