Abstract: A general penalized likelihood hazard estimation procedure is formulated and an asymptotic theory developed. The life time data may be left-truncated, partly right-censored, and may come with a covariate. In the presence of a covariate, the modular model construction via tensor-product splines provides rich collections of hazard models, of which the proportional hazard model and a model of Zucker and Karr (1990) are special cases. The counting process interpretation of life time data and the associated martingale structure are employed in the analysis. Asymptotic convergence rates in a certain symmetrized Kullback-Leibler divergence and in a related mean square error are obtained. A computable adaptive estimate is proposed and is shown to share the same asymptotic convergence rates. A few examples are presented in some detail.
Key words and phrases: Covariate, hazard, Kullback-Leibler divergence, left-truncation, convergence rate, right-censoring, smoothing.