Estimation from aggregate data

A statistical methodology to handle aggregate data is proposed. Aggregate data arise in many fields such as medical science, ecology, social science, reliability, etc. They can be described as follows: individuals are moving progressively along a finite set of states and observations are made in a time window split into several intervals. At each observation time, the only available information is the number of individuals in each state and the history of each item viewed as a stochastic process is thus lost. The time spent in a given state is unknown. Using a data completion technique, an estimation of the hazard rate in each state based on sojourn times is obtained and an estimation of the survival function is deduced. These methods are studied through simulations and applied to a data set. The simulation study shows that the algorithms involved in the methods converge and are robust.