UC Riverside

My dissertation consists of six essays which contribute new theoretical results

to two econometrics frontiers: nonparametrics and finite sample econometrics. Chapters 2 to 3 discuss the estimation and inference of the nonparametric and semiparametric models. In chapter 2 an efficient two-step estimator is developed in single nonparametric regression model with a general parametric error covariance. By fully utilizing the information incorporated in the error covariance into estimation, the newly developed method is more efficient compared to the conventional local linear estimator (LLLS) and some other two-step estimator. The corresponding asymptotic theorems are derived. Monte Carlo study shows the relative efficiency gain of the newly proposed estimator. Chapter 3 systematically develops a new set of results for seemingly unrelated regression (SUR) analysis within nonparametric and semiparametric framework. We study the properties of LLLS and local linear weighted least squares (LLWLS) estimators, provide an efficient two-step estimation for the system and establish the asymptotic theorems under both unconditional and conditional error variance-covariance cases. The procedures of estimation for various nonparametric and semiparametric SUR models are proposed. In addition, two nonparametric goodness-of-fit measures for the system are given. Chapter 4 applies the estimation method developed in chapter 2 and 3 to an empirical analysis on return to public capital in U.S.

Chapters 5 to 6 study the finite sample properties of the mean reversion parameter estimator in continuous time models. In chapter 5 we approximate the bias of the estimator for the Levy-based Ornstein-Uhlenbeck (OU) process, and propose bias corrected estimators. In chapter 6 the exact distribution of the MLE is investigated under different scenarios: known or unknown drift term, fixed or random start-up value, and zero or positive . The numerical calculations demonstrate the remarkably reliable performance of the proposed exact approach.

In chapter 7 we study the efficiency of the coefficient of determination based on

final prediction error and compare it with conventional goodness-of-fit measures

in linear regression models with both normal and non-normal disturbances. The

efficiency results show that R2 based on

final prediction error has practical use in empirical analysis, for examples,

panel data analysis and time series analysis.