Semiparametric models based on transformations and extremes Kjell Doksum Statistics Department University of California, Berkeley and University of Wisconsin, Madison Abstract
The proportional hazard model can be derived as the
survival distribution of a unit whose survival depends on the survival
of a fixed number of components. Nabeya and Miura (NAMI)(1972) describe
the
distribution of a unit whose survival depends on the survival of a
random number of components, where the distribution of the number of
components has a zero truncated Poisson distribution. The partial
likelihood for a NAMI survival regression model is derived and compared
to the partial likelihood for the proportional hazard model. The
proportional hazard likelihood heavily weights the large survival times
while the NAMI likelihood weights survival times more evenly. The
proportional hazard model can also be interpreted as a linear
transformation model with extreme value errors. We consider other
transformation models including models where the response and
covariates are transformed jointly by nonparametric transformations.
