While many coherent fiducial distributions coincide with confidence distributions or Bayesian posterior distributions, there is a general class of coherent fiducial distributions that equates the two-sided p-value with the probability that the null hypothesis is true. The use of that class leads to point estimators and interval estimators that can be derived neither from the dominant frequentist theory nor from Bayesian theories that rule out data-dependent priors. These simple estimators shrink toward the parameter value of the null hypothesis without relying on asymptotics or on prior distributions.

]]>model sometimes does not hold in practice. In this paper, a semi-parametric generalization of the Cox model that permits crossing hazard curves is described. This model allows the interaction between covariates and the baseline hazard, and has been the subject of recent investigation. It includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach cannot be applied here to estimate the model parameters, and flexible methods based on splines and sieves for approximating the baseline hazard have been suggested. A theoretical framework for estimation in this generalized model is developed based on penalized likelihood methods. It is shown that the optimal solution to the baseline hazard, baseline cumulative hazard and their ratio are exponential splines with knots at the unique failure times. Its relationship to prior computational approaches for this model is outlined. ]]>