Technical Reports

This manuscript presents an approximation to the distribution function of a smooth transformation of a random vector, conditional on the event that values of other smooth transformations of the same random vector lie in a small rectangle. This approximation is used to justify the application of standard saddlepoint conditional tail area approximations in circumstances more general than continuous and lattice cases currently justified in the literature. Applications to conditional inference are discussed.

2004-002: Minimum distance estimation for the logistic regression model, by Howard D. Bondell [10/13/04]

It is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations. Several robust alternatives have been proposed. However, upon considering the model via the case-control viewpoint, it is clear that current techniques can exhibit poor behavior in many common situations. A new robust class of estimation procedures is introduced. The estimates are constructed via a minimum distance approach after identifying the model with a semi-parametric biased sampling model. The approach is developed under the case-control sampling scheme yet is shown to be applicable under prospective sampling as well. A weighted Cramer-von Mises distance is used as an illustrative example of the methodology. An affine-invariant version of the goodness-of-fit test of Qin & Zhang (1997) is also discussed.

2004-003: Coupled EM algorithm for multinomial mixture models, by Juan K. Lin [12/30/04]

A new approach to finding good local maxima of the likelihood function based on synthesizing information from two local maxima is presented. We investigate the coupled EM algorithm (CoEM) for coupling local maxima solutions from two separate EM runs. The CoEM algorithm splits and merges multiple latent states based on conditional independence assumptions and is numerically shown to significantly improve on uncoupled EM local maxima solutions.