Some nonparametric regression techniques for complex survey data

In last four decades, the theory of regression analysis in the field of survey data has proven itself to be very useful. Nonparametric regression techniques for survey data analysis though was under-utilized until Bellhouse and Stafford (2001) in which a local polynomial regression technique for complex survey data was established. The main contribution of my thesis is to adapt and develop more nonparametric regression estimation techniques to complex survey data. The secondary contribution of my thesis is developing a graphical diagnostic tool called shift function plot for conducting hypotheses tests involved in the parametric regression models, with the assistance of nonparametric regression techniques.; Chapter 1 gives an overview of the asymptotic aspects of survey sampling. To complete the family of asymptotic theory in the survey sampling, we derive the asymptotic properties of the domain mean.; Chapter 2 summarizes the design-based regression theory, including the asymptotic properties of least squares estimation. With the introduction of the local polynomial regression estimation technique, we extend the asymptotic properties by providing the asymptotic normality of the estimator of the regression function.; In Chapter 3, a partial linear semiparametric regression model is developed for complex surveys. In this semiparametric model, the explanatory variables are represented separately as a nonparametric part and a parametric linear part. The estimation techniques combine nonparametric local polynomial regression estimation in complex surveys and least squares estimation. The setup of the semiparametric regression model reduces the dimension of the nonparametric regression function to avoid the "curse of dimensionality". The main issues related to the these topics have been solved. In particular, we derive the estimates and their moment properties. Asymptotic results such as consistency and normality of the estimates of regression coefficients and the regression functions have also been developed.; The objective of Chapter 4 is to introduce a new graphical approach, called the shift function plot, with which a hypothesis test is constructed to evaluate the goodness of fit of a parametric regression model. For both independent and identically distributed data and complex survey data, we have established the asymptotic properties of the estimators of the shift functions.