Abstract: This study introduces a penalized nonparametric maximum likelihood estimation of the log-hazard function for analyzing right-censored data. Smoothing splines are employed for a smooth estimation. Our main discovery is a functional Bahadur representation, which serves as a key tool for nonparametric inferences of an unknown function. The asymptotic properties of the resulting smoothing-spline estimator of the unknown log-hazard function are established under regularity conditions. Moreover, we provide a local confidence interval for this function, as well as local and global likelihood ratio tests. We also discuss the asymptotic efficiency of the estimator. The theoretical results are validated using extensive simulation studies. Lastly, we demonstrate the estimator by applying it to a real data set.

Key words and phrases: Functional Bahadur representation, likelihood ratio test, nonparametric inference, penalized likelihood, right-censored data, smoothing splines.