A bivariate interval censorship model for partnership formation

We consider a statistical problem of estimating a bivariate age distribution of newly formed partnership. The study is motivated by a type of data that consist of uncensored, right-censored, left-censored, interval-censored and missing observations in the coordinates of a bivariate random vector. A model is proposed for formulating such type of data. A feasible algorithm to estimate the generalized MLE (GMLE) of the bivariate distribution function is also proposed. We establish asymptotic properties for the GMLE under a discrete assumption on the underlying distributions and apply the method to the data set.