  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.
