textIn this dissertation, I would like to consider the efficient estimation of
various models in the presence of heteroskedasticity of unknown form. The first
essay focuses on mean sqaure errors comparison of linear regression model of
hetetroskedasticity with unknown form. I compare higher order properties of
the efficient estimators which include the GMM-type Cragg estimator, FGLS
based on series and kernel estimations. The comparison is to calculate the
approximate mean square errors of estimators using the Nagar type stochastic
expansion.
In the second essay, I consider the efficient estimation of partial linear
regression model under heteroskedastictiy with unknown form. I propose an
efficient estimator and prove it achieves Chamberlain’s (1992) semi-parametric
efficiency bound. The new estimator I propose has the same first order asymptotic properties as Li’s (2000) estimator. My estimator has the potential advantage of analyzing the higher order asymptotics. The third essay considers the two-step series estimation method for
generated regressors problem in context of semiparametric regression model
under heteroskedastictiy of unknown form. I establish the root-n consistency
and asymptotic normality results of the two-step series estimators. Compared
to the double kernel estimator introduced by Stengos and Yan (2001), my
estimator has some computational advantage and is more accurate in the sense
of the asymptotic variance. Simulation results show that the two-step series
estimator outperforms the double kernel estimator in terms of mean absolute
bias and mean square error.
The estimators considered in three essay involve the problem of choosing smoothing parameters. Therefore, I also demonstrate how to pick optimal
smoothing parameters in each essay.Economic