|dc.description.abstract||In this dissertation I investigate several topics in the field of nonparametric econometrics.
In chapter II, we consider the problem of estimating a nonparametric regression
model with only categorical regressors. We investigate the theoretical properties
of least squares cross-validated smoothing parameter selection, establish the rate of
convergence (to zero) of the smoothing parameters for relevant regressors, and show
that there is a high probability that the smoothing parameters for irrelevant regressors
converge to their upper bound values thereby smoothing out the irrelevant regressors.
In chapter III, we consider the problem of estimating a joint distribution defined
over a set of discrete variables. We use a smoothing kernel estimator to estimate the
joint distribution, allowing for the case in which some of the discrete variables are
uniformly distributed, and explicitly address the vector-valued smoothing parameter
case due to its practical relevance. We show that the cross-validated smoothing
parameters differ in their asymptotic behavior depending on whether a variable is
uniformly distributed or not.
In chapter IV, we consider a k-n-n estimation of regression function with k selected
by a cross validation method. We consider both the local constant and local linear cases. In both cases, the convergence rate of of the cross validated k is established.
In chapter V, we consider nonparametric estimation of regression functions with
mixed categorical and continuous data. The smoothing parameters in the model are
selected by a cross-validation method. The uniform convergence rate of the kernel
regression function estimator function with weakly dependent data is derived.||en