Variance estimation for survey estimators that include modeling relies on approximations that ignore the effect of fitting the models. Cross-validation (CV) criterion provides a way to incorporate this effect. We will show 4 ways in which we explore this in this dissertation.

Penalized spline regression, as a main type of nonparametric model assisted methods, is a common technique to improve the precision of finite population estimators. In Chapter 1, we propose a CV based criterion to select the smoothing parameter for the penalized spline regression estimator. The design-based asymptotic properties of the method are derived, and simulation studies show how well it works in practice.

Regression estimator is a common technique to improve the precision of finite population estimators by using the available auxiliary information of the population. In Chapter 2, we propose a CV based variance estimator and compare it to other two variance estimators. The design-based asymptotic properties of the estimator are derived, and simulation studies show how well it works in practice.

Regression estimator works well for the cases where there is a strong linear relationship between regressor and regressands. On the contrary, when the relationship is weak, π estimator is a good choice. In Chapter 3, a new estimator as a linear combination of those two estimators is proposed to select between them. We introduce a CV based variance estimator for the new proposed estimator. The design-based asymptotic properties of the estimator are explored, and simulation studies show how well it works in practice.

In linear regression estimation, how to choose the set of control variables x is a difficult practical problem. In Chapter 4, a CV criterion is introduced for choosing between combinations of the x variables to be included in the model. The design-based asymptotic properties of the estimator are explored, and simulation studies show how well it works in practice.