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Description:
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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 . |