Yanqin Fan

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


This dissertation consists of three essays related to the estimation of econometric models with dependent heterogeneous observations. The first presents a unified overview of the properties of three typical classes of dependent heterogeneous processes. The next two investigate the properties of econometric estimators applied to data generated by such processes.;The most general class of stochastic processes which are asymptotically uncorrelated under certain conditions is the class of L{dollar}\sp{lcub}q{rcub}{dollar}-mixingales for 1 {dollar}\leq q\leq{dollar} 2, which include as special cases both mixing processes and functions of mixing processes. The first essay reviews the two most important properties associated with these three types of stochastic processes, emphasizing their applications in nonparametric time series estimation.;Since there are a number of different nonparametric regression estimators which can be written as linear weighted averages of observations on the dependent variable, the second essay discusses the asymptotic properties of this general class of regression estimators under the assumption that the observations are generated from an L{dollar}\sp{lcub}q{rcub}{dollar}-mixingale for 1 {dollar}\leq q\leq{dollar} 2, which allows for the presence of considerable temporal dependence as well as heterogeneity in the observations. The results obtained in this essay extend and unify those existing in the literature. This essay also provides a direct application of mixingales to the nonparametric literature.;The third examines the asymptotic and finite sample properties of OLS estimators in models with integrated and polynomial trend regressors. The asymptotic results are derived by using the Functional Central Limit Theorem (FCLT). They show that, under certain assumptions, the classical inference procedures based on the asymptotic normality of the underlying estimators are not invalidated by the presence of such regressors. However, the asymptotic distribution may not always provide a useful approximation to the small sample distribution.



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