MSI Weekly Bulletin - Week starting Monday 30 July, 2007

The weaknesses of established model selection procedures based on hypothesis testing and related approaches are discussed. They are contrasted with composite estimation in which the estimators based on the candidate models are combined. The search for a good model, even if effectively conducted, is not conducive to efficient estimation because of the conflict between the probability-related model search and our assessment of efficiency by the mean-squared error. An estimator based on a minimal valid model may be unbiased, but an estimator based on its invalid submodel may be more efficient, because its bias is more than compensated by the variance reduction. Simple examples will be discussed, including with small-area estimation, an application in which composition is used as a matter of course.