Simultaneous Selection of Designs and Models for Optimal Forecasting in Possibly Misspecified Polynomial Regressions

• Activity Number: 655
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Hsiang-Ling Hsu*+ and Mong-Na Lo Huang and Ching-Kang Ing
• Companies: Academia Sinica and National Sun Yat-sen University and Institute of Statistical Science Academia Sinica, Taiwan
• Keywords: Information Criterion ; Model Misspecification ; Model Selection ; Optimal Design

Abstract

The classical optimal design methods have the capability of determining designs to achieve estimation or prediction efficiency in situations where the working model is correctly specified. However, it is unlikely that the designs have the optimal properties when the model is wrong. While the dilemma can be somewhat relieved by considering a set of candidate models and applying a model selection approach to choose the most proper one, it is still difficult to claim the true model is included among the candidate set. Hence an optimal design method that considers model misspecification is called for. A three-stage process is proposed to combine designs and models for optimal prediction. Firstly, a model selection criterion is devised to choose the model having the best prediction capability regardless of whether the true model is one of the candidate models. Secondly, a design selection criterion is given to determine the most appropriate design under the selected model. Finally, a data splitting/merging strategy is given to enhance the prediction power of the model-design combination. The advantages of the proposed method are illustrated via theoretical justification and simulations.