Title: Nonparametric predictive inference for discrete time survival data related to the actuarial estimator
Authors: Ali Mahnashi - Durham University (United Kingdom) [presenting]
Frank Coolen - Durham University (UK)
Tahani Coolen-Maturi - Durham University (United Kingdom)
Abstract: The hazard function is the most common representation of the event time distribution. In discrete time, the hazard at time $t_j$ is defined as the conditional probability that a randomly selected individual will experience the event at time $t_j$, given that the individual did not experience the event prior to $t_j$. The discrete-time hazard can be estimated by the actuarial estimator of the hazard function. Nonparametric predictive inference (NPI) is a frequentist statistics method based on only few assumptions. It focuses explicitly on future observations and uses imprecise probabilities to quantify uncertainty. NPI has been presented for Bernoulli data as well as for right-censored data. We utilise the NPI lower and upper probabilities for Bernoulli data for the actuarial estimator. This development leads us to derive the NPI lower and upper survival functions for the next discrete random variable. Then we compare the discrete-time NPI lower and upper survival functions with the NPI lower and upper survival functions for right censored data in the continuous time case. Furthermore, we aim to develop the discrete-time NPI lower and upper probabilities for multiple discrete random variables. Finally, we use an illustration example to clarify our contribution.