×

Conditions for convergence of Monte Carlo \(EM\) sequences with an application to product diffusion modeling. (English) Zbl 0955.91050

Summary: 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 \(EM\) \((MCEM)\) 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 \(MCEM\) sequence and (ii) primitive conditions for almost-sure monotonicity and almost-sure convergence of an \(MCEM\) 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.

MSC:

91B82 Statistical methods; economic indices and measures
91B26 Auctions, bargaining, bidding and selling, and other market models
PDFBibTeX XMLCite
Full Text: DOI