Nonparametric density estimation for censored survival data: Regression‐spline approach

Abstract

AbstractA method for nonparametric estimation of density based on a randomly censored sample is presented. The density is expressed as a linear combination of cubic M ‐splines, and the coefficients are determined by pseudo‐maximum‐likelihood estimation (likelihood is maximized conditionally on data‐dependent knots). By using regression splines (small number of knots) it is possible to reduce the estimation problem to a space of low dimension while preserving flexibility, thus striking a compromise between parametric approaches and ordinary nonparametric approaches based on spline smoothing. The number of knots is determined by the minimum AIC. Examples of simulated and real data are presented. Asymptotic theory and the bootstrap indicate that the precision and the accuracy of the estimates are satisfactory.