An Objective Measure of Distributional Estimability as Applied to the Phase-Type Aging Model

Cong Nie, Xiaoming Liu and Serge B. Provost ()
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Cong Nie: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, Canada
Xiaoming Liu: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, Canada
Serge B. Provost: Department of Statistical and Actuarial Sciences, The University of Western Ontario, London, ON N6A 5B7, Canada

Risks, 2024, vol. 12, issue 2, 1-26

Abstract: 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.

Keywords: parameter estimation; phase-type aging model; identifiability; estimability (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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