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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4298 |
| Date | 30 October 2006 |
| Creators | Ouyang, Desheng |
| Contributors | Li, Qi |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 479010 bytes, electronic, application/pdf, born digital |
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