PhD Oral Exam - Yajing Zhu, Economics
When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.
Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.
This thesis investigates three topics in theoretical econometrics: goodness-of-fit tests for copulas, copula density estimators which preserve the copula property, and bias-correction for the naive kernel local linear estimators in the two-sample varying coefficient model with missing data. In the first topic a family of goodness-of-fit tests for copulas is proposed. The tests use generalizations of the information matrix equality of White (1982). The asymptotic distribution of the generalized tests is derived. In Monte Carlo simulations, the behavior of the new tests is compared with several Cramer-von Mises type tests and the desired properties of the new tests are confirmed in high dimensions. In the second topic, a semi-parametric copula density estimation procedure that guarantees that the estimator is a genuine copula density is outlined. A simulation-based study is constructed to examine the performance of the proposed copula density estimation method and compare it with the leading copula density estimators in the literature. The method is also applied to estimate copula densities in two empirical cases. The third topic shows that the naive kernel estimator using matching data is not consistent in the two-sample varying coefficient model with missing data. A bias-corrected consistent estimator is proposed and the asymptotic theory is discussed. A simulation study is conducted to support the theoretical results.