Nonparametric recovery of duration distrbutions from cross-sectional sample surveys

Abstract

When lifetimes consist of two phases, and information about a population must be based on a cross-sectional sample, it is sometimes possible to estimate nonparametrically the phase duration distributions, even though the phase durations themselves are not observed. The key requirements are that the process sampled must be stationary, and that the observations at the time of cross-section include the age and phase of each sampled lifetime at the time of sampling. The estimation procedures must allow for length-bias even when the relevant lengths are not recorded. Stronger results are available when certain parametric assumptions are satisfied about the relationship of the phase durations to the total lifetime, or alternatively when it is also possible to record the total lifetime from a follow-up survey.

Keywords:

• cross-sectional sampling
• length bias
• censored survival data
• nonparametric density estimation
• duration distributions