ruth@utstat.uucp (Ruth Croxford) (02/21/90)
Topic: Mixture Models as Applied to Models Involving Many Incidental Parameters Speaker: Mary Lesperance, McMaster University Date: 4:00 - 5:00 p.m., Thursday, March 1, 1990 Place: Room 1085, Sidney Smith Hall, 100 St. George Street, U of T Abstract: Statistical models which contains many incidental (or nuisance) parameters arise naturally in many disciplines, and it is well known that the method of maximum likelihood can perform poorly with these models. In response, several authors have derived alternative likelihood methods for estimating structural parameters in models which contain many incidental parameters. In particular, Kiefer & Wolfowitz (1956) consider the incidental parameters to be independent random variates with common unknown distribution function, say G. This yields a mixture model for the data y, f(y | phi, G) = int (p(y | phi, theta) dG(a), a function of the structural parameter phi, and G, the mixing distribution. Kiefer & Wolfowitz's assumptions are highly restrictive, however, and it is shown that the mixture model approach is more widely applicable to models that are commonly used in many applications. maximum likelihood estimates of structural parameters derived from the mixture likelihood are sensible Kiefer & Wolfowitz (1956) did not address the practical aspects of computing the maximum likelihood estimates of their model parameters, phi and G. Note that G is not assumed to belong to a parametric family, and so, computing the mle of G involves finding the arbitrary distribution G hat which maximizes the likelihood. Since Kiefer & Wolfowitz's work, several suggestions have been proposed in the mixture model literature for computation of the nonparametric mle of the mixing distribution G. These procedures, however, tend to be slow, and impractical to use while simultaneously maximizing the likelihood over the parameter space. A new algorithm for computing the nonparametric mle of G is described. The algorithm is more efficient in terms of computation time that those described hitherto. -------------- Coffee and tea will be served in the DeLury Lounge (SS6006) at 3:30 p.m. estimates in all examples considered.