This paper derives some uniform convergence rates for kernel regression of some index functions that may depend on infinite dimensional parameter. The rates of convergence are computed for independent, strongly mixing and weakly dependent data respectively. These results extend the existing literature and are useful for the derivation of large sample properties of the estimators in some semiparametric and nonparametric models.
We investigate the finite sample performance of several estimators proposed for the panel data Tobit regression model with individual effects, including Honor6 estimator, Hansen＇s best two-step GMM estimator, the continuously updating GMM estimator, and the empirical likelihood estimator （ELE）. The latter three estimators are based on more conditional moment restrictions than the Honor6 estimator, and consequently are more efficient in large samples. Although the latter three estimators are asymptotically equivalent, the last two have better finite sample performance. However, our simulation reveals that the continuously updating GMM estimator performs no better, and in most cases is worse than Honor6 estimator in small samples. The reason for this finding is that the latter three estimators are based on more moment restrictions that require discarding observations. In our designs, about seventy percent of observations are discarded. The insufficiently few number of observations leads to an imprecise weighted matrix estimate, which in turn leads to unreliable estimates. This study calls for an alternative estimation method that does not rely on trimming for finite sample panel data censored regression model.
