Marker dependent kernel hazard estimation from local linear estimation

Abstract

Marker dependent hazard estimation based on weighted least square local linear and local constant kernel estimation is considered, and the nonparametric marker dependent hazard estimator of Nielsen (1992) and Nielsen & Linton (1995) is identified as a local constant estimator. The method is related to local linear fitting known from regression estimation, e.g. Fan & Gijbels (1996), and density estimation, e.g. Jones (1993). We derive the pointwise asymptotic theory. Through the introduction of a second order stochastic kernel, the bias considerations of the local linear estimator turn out to be simpler than the bias considerations of the local constant estimator. We also consider the marker-only case applied by Fusaro et al. (1993) while investigating onset of AIDS.

Key words:

• Counting process theory
• kernel estimation
• marker dependent hazards
• local linear fitting
• boundary correction