Penalized Likelihood Estimation of Hazard and Intensity Functions

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1987 · Volume 49 · Issue 2

DOI: 10.1111/j.2517-6161.1987.tb01688.x

Abstract

A nonparametric estimate is proposed for the hazard function using penalized likelihood methods. The estimate turns out to be a hyperbolic spline function which is continuous with its first derivative discontinuous only at a finite number of points. It always assumes positive values, unlike Anderson and Senthilselvan's (1980) quadratic spline estimate. This method is modified for the estimation of the intensity function of a nonstationary Poisson process. An example is given for comparison of the new estimator with the estimator of Anderson and Senthilselvan (1980).

Keywords

penalized likelihood estimation, nonparametric hazard function estimation, censored data, spline function, smoothness parameter, nonparametric estimation of intensity function, nonstationary poisson process, stanford heart transplant data

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