Nonparametric estimation of econometric models with categorical variables
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.
Citation
Ouyang, Desheng (2005). Nonparametric estimation of econometric models with categorical variables. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /4298.