We introduce a covariate-specific total variation penalty in two
semiparametric models for the rate function of recurrent event process. The two
models are a stratified Cox model, introduced in Prentice et al. (1981), and a
stratified Aalen's additive model. We show the consistency and asymptotic
normality of our penalized estimators. We demonstrate, through a simulation
study, that our estimators outperform classical estimators for small to
moderate sample sizes. Finally an application to the bladder tumour data of
Byar (1980) is presented
