Conditions for convergence of Monte Carlo EM sequences with an application to product diffusion modeling

Intractable maximum likelihood problems can sometimes be finessed with a Monte Carlo implementation of the EM algorithm. However, there appears to be little theory governing when Monte Carlo EM (M C E M) sequences converge. Consequently, in some applications, convergence is assumed rather than proved. Motivated by this problem in the context of modeling market penetration of new products and services over time, we develop (i) high-level conditions for rates of almost-sure convergence and convergence in distribution of any M C E M sequence and (ii) primitive conditions for almost-sure monotonicity and almost-sure convergence of an M C E M sequence when Monte Carlo integration is carried out using independent Gibbs runs. We verify the main primitive conditions for the Bass product diffusion model and apply the methodology to data on wireless telecommunication services.