An objective measure of distributional estimability as applied to the phase-type aging model

The phase-type aging model (PTAM) is a class of Coxian-type Markovian models that can provide a quantitative description of the effects of various aging characteristics. Owing to the unique structure of the PTAM, parametric inference on the model is affected by a significant estimability issue, its profile likelihood functions being flat. While existing methods for assessing distributional non-estimability require the subjective specification of thresholds, this paper objectively quantifies estimability in the context of general statistical models. More specifically, this is achieved via a carefully designed cumulative distribution function sensitivity measure, under which the threshold is tailored to the empirical cumulative distribution function, thus becoming an experiment-based quantity. The proposed definition, which is validated to be innately sound, is then employed to determine and enhance the estimability of the PTAM.