A comparative study of nonparametric estimation in Weibull regression: A penalized likelihood approach

The Weibull distribution is popularly used to model lifetime distributions in many areas of applied statistics. This paper employs a penalized likelihood method to estimate the shape parameter and an unknown regression function simultaneously in a nonparametric Weibull regression. Four methods were considered: two cross-validation methods, a corrected Akaike information criterion, and a Bayesian information criterion. Each method was evaluated based on shape parameter estimation as well as selecting the smoothing parameter in a penalized likelihood model through a simulation study. Adapting a lower-dimensional approximation and deriving confidence intervals from Bayes models of the penalized likelihood, the comparative performances of methods using both censored and uncensored data were examined for various censoring rates. The methods are applied to a real data example of lung cancer.