Estimation of reinforced urn processes under left-truncation and right-censoring

We propose a nonparametric estimator for bivariate left-truncated and
right-censored (LTRC) observations that combines the
Expectation-Maximization (EM) algorithm and the Reinforced Urn Process
(RUP). The resulting Expectation-Reinforcement (ER) algorithm allows for
the inclusion of experts' knowledge in the form of a prior
distribution, thus belonging to the class of Bayesian models. This can be
relevant in applications where the data is incomplete, due to biases in
the sampling process, as in the case of left-truncation and
right-censoring. With this new approach, the distribution of the
truncation variables is also recovered, granting further insight into
those biases, and playing an important role in applications like prevalent
cohort studies. The estimators are tested numerically using artificial and
empirical datasets and compared with other methodologies such as copula
models and the Kaplan-Meier estimator.