Abstract:  Applied econometric analysis is often performed using data collected from large-scale surveys. These surveys use complex sampling plans in order to reduce costs and increase the estimation eciency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population and dependent observations within the sample, violating the asumtion that the data is independently and identically distributed. The purpose of this chapter is to derive the asymptotic properties of a probability weighted nonparametric regression estimator under a combined inference framework. The nonparametric regression estimator considered is the local constant estimator. This work contributes to the literature in three ways. First, it derives the asymptotic properties for the multivariate mixed data case, including the asymptotic normality of the estimator. Second, I consider settings where the data in the population are iid and weakly correlated within clusters and show that the leading terms for the mean squared error are the same in both cases. Finally, I use least squares cross-validation for selecting the bandwidth for both continuous and discrete variables. I run Monte Carlo simulations designed to assess the nite-sample performance of the probability weighted local constant estimator versus the traditional local constant estimator for three sampling methods: simple random sampling, exogeneous stratication, and endogeneous stratication. Simulation results show that the estimator is consistent and that eciency gains can be made by weighting observations by the inverse of their inclusion probabilities if the sampling is endogeneous.

 

 

Abstract: The literature on nonparametric instrumental variable (IV) methods has been growing, and while the mathematics behind these methods are highly technical, researchers believe that these methods will soon emerge as viable alternatives to parametric approaches. The difficulty of these methods stems from the fact that the nonparametric instrumental variable estimator is the solution to a ill-posed inverse problem. The ill-posed inverse problem is solved by using regularization methods. Therefore there are two steps for solving the nonparametric (IV) problem: estimating conditional means and regularization. When analysis is performed using complex survey data, one must also consider the sampling design. When endogeneous sampling is present, traditional estimation methods will be inconsistent. I extend the theory of nonparametric IV models to account for sample design by estimating the conditional mean functions using a probability weighted local constant estimator. The example chosen is an update on the paper by Mulvale and Hurley (2008), who studied the effects of private prescription drug insurance on the use of pharmaceuticals, using the marginal tax rate as an instrument.

 

 

Abstract: Many variables derived from survey responses are discrete. When the outcome variable in a regression model is discrete, estimates represent the probability that the outcome variable takes on a certain value. Large scale surveys often use complex sampling plans to lower costs of implementing a survey and increase the precision of subgroups of the population. These complex sampling plans lead to unequal inclusion probabilities; ignoring the sampling design can lead to inconsistent results. Weighting observations by the inverse of their inclusion probabilities corrects for endogeneous sampling and improves the efficiency of estimators. I propose estimating conditional probability density function using probability weighted kernel density estimators. 

• 2014-2015 - Research Assistant, Professor Rick Audas, Memorial University of Newfoundland
• 2012 - Research Assistant, Professor Doug May, Memorial University of Newfoundland