Many of these models impose the assumptions that heterogeneity is independent of the observed covariates, it has a distribution that depends on a finite number of parameters only, and it enters the hazard function multiplicatively.
[3] In the general case, the cumulative distribution function of ti* associated with the conditional hazard is given by F(t|xi , vi ; θ).
Under the first assumption above, the unobserved component can be integrated out and we obtain the cumulative distribution on the observed covariates only, i.e. G(t ∨ xi ; θ , ρ) = ∫ F (t ∨ xi, ν ; θ ) h ( ν ; ρ ) dν [4] where the additional parameter ρ parameterizes the density of the unobserved component v. Now, the different estimation methods for stock or flow sampling data are available to estimate the relevant parameters.
[6] Recent examples provide a nonparametric approaches to estimating the baseline hazard and the distribution of the unobserved heterogeneity under fairly weak assumptions.
[7] In grouped data, the strict exogeneity assumptions for time-varying covariates are hard to relax.