Nonparametric Information Criterion for Model-Assisted Survey Estimators

• Activity Number: 400
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Addison James*+ and Lan Xue and Virginia Lesser
• Companies: and Oregon State University and Oregon State University
• Keywords: Nonparametric ; Survey ; Finite Population ; Splines ; Model-Assisted ; Variable Selection

Abstract

Nonparametric model-assisted estimators were recently proposed to improve estimates of finite population parameters. This results in more efficient estimators when the parametric model is misspecified. In this paper, we propose a nonparametric information criterion to select appropriate auxiliary variables to use in an additive model-assisted method. We approximate the additive nonparametric components by polynomial splines and extend the nonparametric Bayesian Information Criterion (BIC) for finite populations. By removing irrelevant auxiliary variables, our method not only reduces model complexity, but also decreases estimator variance. We establish that the proposed nonparametric BIC is asymptotically consistent in selecting the correct variables, which is also confirmed by our numerical study. Our proposed method is easier to implement and theoretically justified compared with a two-step procedure proposed in Wang and Wang (2011).