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This dissertation provides a thorough overview of the use of nonparametric estimation methods for analyzing data collected by complex sampling plans. Applied econometric analysis is often performed using data collected from large-scale surveys, which use complex sampling plans in order to reduce administrative costs and increase the estimation efficiency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population. If one is interested in estimating descriptive statistics, it is highly recommended that one uses an estimator that weights each observation by the inverse of the unit's probability of being included in the sample. If one is interested in estimating causal effects, a weighted estimator should be used if the sampling criterion is correlated with the error term. The sampling criterion is the variable used to design the sampling scheme. If it is correlated with the error term, sampling is said to be endogenous and, if ignored, leads to inconsistent estimation. I consider three distinct probability weighted estimators: i) a nonparametric kernel regression estimator; ii) a conditional probability distribution function estimator; and iii) a nonparametric instrumental variable regression estimator. / Thesis / Doctor of Philosophy (PhD)

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published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In this thesis, we try to provide a broad econometric analysis of a class of risk measures, distortion risk measures (DRM). With carefully selected functional form, the Value-at-Risk (VaR) and Tail-VaR (TVaR) are special cases of DRMs. Besides, the DRM also admits interpretation in the sense of non-expected utility type of preferences. We first provide a unified statistical framework for the nonparametric estimators of the DRMs in a univariate case. The asymptotic properties of both the DRMs and their sensitivities with respect to the parameters representing risk aversion and/or pessimism are derived. Moreover, the relationships between the VaR and TVaR are also investigated in detail, which, we hope, can shed new lights on the way passing one risk measure to another. Then, the analysis of DRMs are extended to a multi-dimensional framework, where the DRM is computed for a portfolio consisting of many primitive assets. Analogous to the mean-variance frontier analysis, we study the efficient portfolio frontier when both objective and constraint are replaced by the DRMs. We call this the DRM-DRM framework. Under a nonparametric setting, we propose three asymptotic test statistics for evaluating the efficiency of a given portfolio. Finally, we discuss the criteria used for evaluating models used to forecast the VaRs. More precisely, we propose a criterion which takes into account the loss levels beyond the VaRs.