Information Criterion for Nonparametric Model-Assisted Survey Estimators

Graduation date: 2017Nonparametric model-assisted estimators have been proposed to improve estimates\ud of finite population parameters. More efficient estimators are obtained when the parametric\ud model is misspecified due to the flexibility of nonparametric models. In this\ud dissertation, we derive information criteria to select appropriate auxiliary variables to\ud use in an additive model-assisted method. By removing irrelevant auxiliary variables,\ud our method reduces model complexity and decreases estimator variance. Our proposed\ud Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)\ud account for the sampling design using the first order inclusion probabilities of each\ud element. We approximate the additive nonparametric components using polynomial\ud splines. We establish that the proposed BIC is asymptotically consistent to select the\ud important explanatory variables in a finite population. This result is confirmed by our\ud numerical study under a range of superpopulation models. Our numerical study shows\ud that the AIC tends to overfit and does not show an increase in performance as the sample size increases. Using the BIC, our proposed method is easier to implement and\ud theoretically justified compared with a previously proposed method