Testing Proportionality in Duration Models with Respect to Continuous Covariates

Several omnibus tests of the proportional hazards assumption have been proposed in the literature. In the two-sample case, tests have also been developed against non-parametrically specified ordered alternatives. This paper considers a natural extension of such monotone ordering to the case of continuous covariates, and develops tests for the proportional hazards assumption against such ordered alternatives. Small sample properties of the tests are explored. The use of the test statistics, and use of histogram sieve estimators in the case where proportionality does not hold, are illustrated with application to data on strike durations.