Yuhong Yang

Statistical models (parametric or not) are essential for estimation and prediction. In most practical situations, multiple choices of models are available for consideration. Traditionally, one of the candidate models is selected based on hypothesis testing and/or a model selection criterion (e.g., AIC or BIC), together with proper model assessment (e.g., checking residual plots). Once a model is declared the winner, estimation and prediction are based on it. This approach, however, ignores the model selection uncertainty. When there is not enough evidence to prefer one model to others, the practice of "winner takes all" by selecting a single model is problematic. Alternatively, one can consider combining the candidate models. We have proposed the approach of convex combining, which takes advantage of some information-theoretic tools. The resulting estimators/predictions are theoretically characterized with practical advantage over model selection methods when instability in model selection is non-negligible. Research in this direction has covered density estimation, regression, forecasting, classification and loglinear models. There are a number of basic questions on model combining/selection that are theoretically interesting and practically important. For examples, when does model combining work better than model selection? Can we construct an index that properly guides a practitioner to choose between model selection and model combining? Can model combining solve the conflict between AIC and BIC by achieving both consistency in selection (in the sense that the weight of the best model converges to 1) and also achieving optimality in estimating the target function? How to screen out poor models before combining? What is the price for combining models? What happens when the observations are possibly long-range dependent? We have been trying to answer such questions. Other areas that are of interest to me include gene expression data analysis, sequential design, machine learning and time series forecasting.